JEE Main & Advanced Physics Two Dimensional Motion Question Bank

done Non-uniform Circular Motion Total Questions - 48

• question_answer1)
  In a circus stuntman rides a motorbike in a circular track of radius \[R\] in the vertical plane. The minimum speed at highest point of track will be [CPMT 1979; JIPMER 1997; RPET 1999]
  A)
              \[\sqrt{2gR}\] done clear
  B)
                       \[2gR\] done clear
  C)
              \[\sqrt{3gR}\]   done clear
  D)
              \[\sqrt{gR}\] done clear
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• question_answer2)
  A block of mass \[m\] at the end of a string is whirled round in a vertical circle of radius \[R\]. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is       [DCE 1999, 2001]
  A)
              \[Rg\]   done clear
  B)
              \[{{(Rg)}^{2}}\] done clear
  C)
              \[R/g\]  done clear
  D)
              \[\sqrt{Rg}\] done clear
  View Solution play_arrow

• question_answer3)
  A sphere is suspended by a thread of length \[l\]. What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension  [ISM Dhanbad 1994]
  A)
              \[gl\] done clear
  B)
                       \[2gl\] done clear
  C)
              \[\sqrt{gl}\]      done clear
  D)
              \[\sqrt{2gl}\] done clear
  View Solution play_arrow

• question_answer4)
  A bottle of sodawater is grasped by the neck and swing briskly in a vertical circle. Near which portion of the bottle do the bubbles collect
  A)
              Near the bottom done clear
  B)
              In the middle of the bottle done clear
  C)
              Near the neck done clear
  D)
              Uniformly distributed in the bottle done clear
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• question_answer5)
  A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take \[g=10m/{{\sec }^{2}}\])                               [AIIMS 1987]
  A)
              4 m/sec done clear
  B)
                       6.25 m/sec done clear
  C)
              16 m/sec done clear
  D)
                       None of the above done clear
  View Solution play_arrow

• question_answer6)
          A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle \[{{\theta }_{1}}\]. In the next 2 sec, it rotates through an additional angle \[{{\theta }_{2}}\]. The ratio of \[\sqrt{3}mg\] is                                      [AIIMS 1985]
  A)
              1 done clear
  B)
                       2 done clear
  C)
              3          done clear
  D)
              5 done clear
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• question_answer7)
  A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at (g = 10 m/sec2) [AIIMS 1982]
  A)
              Top of the circle           done clear
  B)
              Bottom of the circle done clear
  C)
              Half way down done clear
  D)
                       None of the above done clear
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• question_answer8)
  A cane filled with water is revolved in a vertical circle of radius 4 meter and the water just does not fall down. The time period of revolution will be                       [CPMT 1985;                                     RPET 1995; UPSEAT 2002; MH CET 2002]
  A)
              1 sec    done clear
  B)
              10 sec done clear
  C)
              8 sec    done clear
  D)
              4 sec done clear
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• question_answer9)
  A 2 kg  stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is                               [AIIMS 1982]
  A)
              At the top of the circle done clear
  B)
              At the bottom of the circle done clear
  C)
              Halfway down done clear
  D)
              None of the above done clear
  View Solution play_arrow

• question_answer10)
  A body slides down a frictionless track which ends in a circular loop of diameter \[D\], then the minimum height \[h\] of the body in term of \[D\] so that it may just complete the loop, is
  A)
              \[h=\frac{5D}{2}\] done clear
  B)
                       \[h=\frac{5D}{4}\] done clear
  C)
              \[h=\frac{3D}{4}\] done clear
  D)
            \[h=\frac{D}{4}\] done clear
  View Solution play_arrow

• question_answer11)
  A car is moving with speed 30 \[m/\sec \]on a circular path of radius 500 m. Its speed is increasing at the rate of \[2m/{{\sec }^{2}},\] What is the acceleration of the car                         [MP PMT 2003; Roorkee 1982; RPET 1996; MH CET 2002]
  A)
              \[2m/{{\sec }^{2}}\] done clear
  B)
                       \[2.7m/{{\sec }^{2}}\] done clear
  C)
              \[1.8m/{{\sec }^{2}}\] done clear
  D)
                       \[9.8\,m/{{\sec }^{2}}\] done clear
  View Solution play_arrow

• question_answer12)
  The string of pendulum of length \[l\] is displaced through \[{{90}^{o}}\] from the vertical and released. Then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is                                                  [MP PMT 1986]
  A)
              \[mg\] done clear
  B)
                       \[3mg\] done clear
  C)
              \[5\,mg\]           done clear
  D)
              \[6\,mg\] done clear
  View Solution play_arrow

• question_answer13)
  A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If \[g=10m/{{s}^{2}}\], then the maximum angular velocity of the stone will be                          [MP PMT 1994]
  A)
              \[5\,\,rad/s\] done clear
  B)
                       \[\sqrt{30}\,rad/s\] done clear
  C)
              \[\sqrt{60}\,rad/s\] done clear
  D)
                       \[10\,rad/s\] done clear
  View Solution play_arrow

• question_answer14)
  A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point such that
  A)
              \[h=R\] done clear
  B)
                       \[h=\frac{R}{3}\] done clear
  C)
              \[h=\frac{R}{2}\]       done clear
  D)
              \[h=\frac{2R}{3}\] done clear
  View Solution play_arrow

• question_answer15)
  A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break [MP PET 1997]
  A)
              When the mass is at the highest point of the circle done clear
  B)
              When the mass is at the lowest point of the circle done clear
  C)
              When the wire is horizontal done clear
  D)
              At an angle of \[{{\cos }^{-1}}(1/3)\] from the upward vertical done clear
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• question_answer16)
  A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g=10\,m{{s}^{-2}}\], then the maximum angular velocity of the stone will be                                      [MP PMT/PET 1998]
  A)
              4 radians/sec done clear
  B)
                       16 radians/sec done clear
  C)
              \[\sqrt{21}\] radians/sec           done clear
  D)
              2 radians/sec done clear
  View Solution play_arrow

• question_answer17)
  The maximum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius \[l\]             [CPMT 1999; MH CET 2004]
  A)
              \[\sqrt{gl}\] done clear
  B)
                       \[\sqrt{3gl}\] done clear
  C)
              \[\sqrt{5gl}\]    done clear
  D)
              \[\sqrt{7gl}\] done clear
  View Solution play_arrow

• question_answer18)
  If the equation for the displacement of a particle moving on a circular path is given by \[(\theta )=2{{t}^{3}}+0.5\], where \[\theta \] is in radians and \[t\] in seconds, then the angular velocity of the particle after 2 sec from its start is                    [AIIMS 1998]
  A)
              8 rad/sec done clear
  B)
                       12 rad/sec done clear
  C)
              24 rad/sec done clear
  D)
                       36 rad/sec done clear
  View Solution play_arrow

• question_answer19)
  A body of mass \[m\] hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of \[{{60}^{o}}\] with the vertical. The tension in the string at mean position is                                   [ISM Dhanbad 1994]
  A)
              \[2\,mg\] done clear
  B)
                       \[mg\] done clear
  C)
              \[3mg\] done clear
  D)
              \[\sqrt{3}mg\] done clear
  View Solution play_arrow

• question_answer20)
  In a vertical circle of radius r, at what point in its path a particle has tension equal to zero if it is just able to complete the vertical circle                                 [EAMCET 1994]
  A)
              Highest point done clear
  B)
              Lowest point done clear
  C)
              Any point done clear
  D)
              At a point horizontally from the centre of circle of radius r done clear
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• question_answer21)
  The tension in the string revolving in a vertical circle with a mass  \[m\] at the end which is at the lowest position [EAMCET (Engg.) 1995; AIIMS 2001]
  A)
              \[\frac{m{{v}^{2}}}{r}\] done clear
  B)
                       \[\frac{m{{v}^{2}}}{r}-mg\] done clear
  C)
              \[\frac{m{{v}^{2}}}{r}+mg\] done clear
  D)
                       \[mg\] done clear
  View Solution play_arrow

• question_answer22)
  A hollow sphere has radius 6.4 m. Minimum velocity required by a motor cyclist at bottom to complete the circle will be                                      [RPET 1997]
  A)
              17.7 m/s done clear
  B)
                       10.2 m/s done clear
  C)
              12.4 m/s done clear
  D)
                       16.0 m/s done clear
  View Solution play_arrow

• question_answer23)
  A block follows the path as shown in the figure from height \[h\]. If radius of circular path is \[r\], then relation that holds good to complete full circle is                  [RPET 1997]
  A)
              \[h<5r/2\] done clear
  B)
                       \[h>5r/2\] done clear
  C)
              \[h=5r/2\] done clear
  D)
                       \[h\ge 5r/2\] done clear
  View Solution play_arrow

• question_answer24)
  A pendulum bob on a 2 m string is displaced 60o from the vertical and then released.  What is the speed of the bob as it passes through the lowest point in its path           [JIPMER 1999]
  A)
              \[\sqrt{2}\,\,m/s\] done clear
  B)
                      \[\sqrt{9.8}\,\,m/s\] done clear
  C)
              4.43 m/s done clear
  D)
                       \[1/\sqrt{2}\,\,m/s\] done clear
  View Solution play_arrow

• question_answer25)
  A fan is making 600 revolutions per minute.  If after some time it makes 1200 revolutions per minute, then increase in its angular velocity is                                    [BHU 1999]
  A)
              \[10\,\pi \,rad/\sec \] done clear
  B)
                       \[20\,\pi \,rad/\sec \] done clear
  C)
              \[40\,\pi \,rad/\sec \] done clear
  D)
                       \[60\,\pi \,rad/\sec \] done clear
  View Solution play_arrow

• question_answer26)
  A particle is tied to 20cm long string.  It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero [RPMT 1999]
  A)
              \[5\,rad/sec\] done clear
  B)
                      \[2\,rad/sec\] done clear
  C)
              \[7.5\,rad/sec\] done clear
  D)
                          \[7\,rad/sec\]             done clear
  View Solution play_arrow

• question_answer27)
  A stone tied with a string, is rotated in a vertical circle.  The minimum speed with which the string has to be rotated                                     [CBSE PMT 1999]
  A)
              Is independent of the mass of the stone done clear
  B)
              Is independent of the length of the string done clear
  C)
              Decreases with increasing mass of the stone   done clear
  D)
                  Decreases with increasing in length of the string done clear
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• question_answer28)
  For a particle in a non-uniform accelerated circular motion                         [AMU (Med.) 2000]
  A)
              Velocity is radial and acceleration is transverse only   done clear
  B)
              Velocity is transverse and acceleration is radial only done clear
  C)
                  Velocity is radial and acceleration has both radial and transverse components            done clear
  D)
                  Velocity is transverse and acceleration has both radial and transverse components done clear
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• question_answer29)
  A fighter plane is moving in a vertical circle of radius ?r?.  Its minimum velocity at the highest point of the circle will be                                     [MP PET 2000]
  A)
              \[\sqrt{3\,g\,r}\] done clear
  B)
                      \[\sqrt{2\,g\,r}\] done clear
  C)
              \[\sqrt{g\,r}\]    done clear
  D)
              \[\sqrt{gr/2}\] done clear
  View Solution play_arrow

• question_answer30)
  A ball is moving to and fro about the lowest point A of a smooth hemispherical bowl.  If it is able to rise up to a height of 20 cm on either side of A, its speed at A must be (Take = 10 m/s2, mass of the body 5 g)                           [JIPMER 2000]
  A)
              0.2 m/s done clear
  B)
                       2 m/s done clear
  C)
              4 m/s   done clear
  D)
              4.5 \[m{{s}^{1}}\] done clear
  View Solution play_arrow

• question_answer31)
  A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolutions per minute.  The total tension in the string when the stone is at its lowest point is               [Kerala (Engg.) 2001]
  A)
              \[mg\] done clear
  B)
                       \[m(g+\pi \,n\,{{r}^{2}})\] done clear
  C)
              \[m(g+\pi \,n\,r)\] done clear
  D)
                       \[m\{g+({{\pi }^{2}}\,{{n}^{2}}\,r)/900\}\] done clear
  View Solution play_arrow

• question_answer32)
  As per given figure to complete the circular loop what should be the radius if initial height is 5 m       [RPET 2001]
  A)
              4 m done clear
  B)
              3 m done clear
  C)
              2.5 m done clear
  D)
              2 m done clear
  View Solution play_arrow

• question_answer33)
  A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre.  If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is                             [CPMT 2001]
  A)
              27 cm done clear
  B)
                       9 cm done clear
  C)
              3 cm    done clear
  D)
              1 cm done clear
  View Solution play_arrow

• question_answer34)
  When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations.  How many more rotation will it make before coming to rest (Assume uniform angular retardation)                                  [KCET 2001]
  A)
              18 done clear
  B)
                       12 done clear
  C)
              36        done clear
  D)
              48 done clear
  View Solution play_arrow

• question_answer35)
  A body crosses the topmost point of a vertical circle with critical speed.  Its centripetal acceleration, when the string is horizontal will be                              [MH CET 2002]  
  A)
              6 g done clear
  B)
                       3 g done clear
  C)
              2 g done clear
  D)
                       g done clear
  View Solution play_arrow

• question_answer36)
  A simple pendulum oscillates in a vertical plane.  When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob.  What is the maximum displacement of the pendulum of the string with respect to the vertical                               [Orissa JEE 2002]
  A)
              \[{{30}^{o}}\]          done clear
  B)
              \[{{45}^{o}}\] done clear
  C)
              \[{{60}^{o}}\]          done clear
  D)
              \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer37)
  A particle is moving in a vertical circle.  The tensions in the string when passing through two positions at angles\[{{30}^{o}}\] and \[{{60}^{o}}\] from vertical (lowest position) are \[{{T}_{1}}\]and \[{{T}_{2}}\]respectively.  then                                  [Orissa JEE 2002]
  A)
               \[{{T}_{1}}={{T}_{2}}\]             done clear
  B)
              \[{{T}_{2}}>{{T}_{1}}\] done clear
  C)
              \[{{T}_{1}}>{{T}_{2}}\]    done clear
  D)
              Tension in the string always remains the same done clear
  View Solution play_arrow

• question_answer38)
  A particle is kept at rest at the top of a sphere of diameter 42 m.  When disturbed slightly, it slides down.  At what height ?h? from the bottom, the particle will leave the sphere                                     [BHU 2003]
  A)
              14 m done clear
  B)
                       28 m done clear
  C)
              35 m    done clear
  D)
              7 m done clear
  View Solution play_arrow

• question_answer39)
  The coordinates of a moving particle at any time ?t? are given by x = at3 and y = bt3.  The speed of the particle at time ?t? is given by                                [AIEEE 2003]
  A)
              \[\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\] done clear
  B)
                       \[3\,t\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\] done clear
  C)
              \[3\,{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\] done clear
  D)
                       \[{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\] done clear
  View Solution play_arrow

• question_answer40)
  A small disc is on the top of a hemisphere of radius \[R\]. What is the smallest horizontal velocity v that should be given to the disc for it to leave the hemisphere and not slide down it ? [There is no friction]               [CPMT 1991]
  A)
              \[v=\sqrt{2gR}\] done clear
  B)
                       \[v=\sqrt{gR}\] done clear
  C)
              \[v=\frac{g}{R}\] done clear
  D)
                       \[v=\sqrt{{{g}^{2}}R}\] done clear
  View Solution play_arrow

• question_answer41)
  A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec.  If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle, is                                     [CBSE PMT 1999]
  A)
              41.56 N done clear
  B)
                       89.86 N done clear
  C)
              109.86 N done clear
  D)
                       115.86 N done clear
  View Solution play_arrow

• question_answer42)
  A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket [AFMC 2004]
  A)
              1 sec    done clear
  B)
            2 sec done clear
  C)
                  3 sec       done clear
  D)
                  4 sec done clear
  View Solution play_arrow

• question_answer43)
  Figure shows a body of mass m moving with a uniform speed v along a circle of radius r. The change in velocity in going from A to B is                                     [DPMT 2004]
  A)
              \[v\sqrt{2}\] done clear
  B)
            \[v/\sqrt{2}\] done clear
  C)
                  \[v\] done clear
  D)
                  Zero done clear
  View Solution play_arrow

• question_answer44)
  The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3 then its velocity is                                   [Pb. PET 2003]
  A)
              \[\sqrt{98}\,\,m/s\] done clear
  B)
                     \[7\,\,m/s\] done clear
  C)
                  \[\sqrt{490}\,\,m/s\] done clear
  D)
                              \[\sqrt{4.9}\] done clear
  View Solution play_arrow

• question_answer45)
  For a particle in circular motion the centripetal acceleration is
  A)
              Less than its tangential acceleration done clear
  B)
              Equal to its tangential acceleration done clear
  C)
              More than its tangential acceleration done clear
  D)
              May be more or less than its tangential acceleration done clear
  View Solution play_arrow

• question_answer46)
  A particle moves in a circular path with decreasing speed. Choose the correct statement.                  [IIT JEE 2005]
  A)
                                  Angular momentum remains constant                               done clear
  B)
                   Acceleration (\[\vec{a}\]) is towards the center             done clear
  C)
               Particle moves in a spiral path with decreasing radius             done clear
  D)
                          The direction of angular momentum remains constant             done clear
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• question_answer47)
  A body of mass 1 kg is moving in a vertical circular path of radius 1m. The difference between the kinetic energies at its highest and lowest position is     
  A)
              20J done clear
  B)
                       10J done clear
  C)
                          \[4\sqrt{5}J\]               done clear
  D)
                          \[10\left( \sqrt{5}-1 \right)J\] done clear
  View Solution play_arrow

• question_answer48)
  The angle turned by a body undergoing circular motion depends on time as \[\theta ={{\theta }_{0}}+{{\theta }_{1}}t+{{\theta }_{2}}{{t}^{2}}\]. Then the angular acceleration of the body is                                   [Orissa JEE 2005]
  A)
              \[{{\theta }_{1}}\]      done clear
  B)
              \[{{\theta }_{2}}\] done clear
  C)
                          \[2{{\theta }_{1}}\]                done clear
  D)
                          \[2{{\theta }_{2}}\]             done clear
  View Solution play_arrow