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question_answer1) Why cannot be vectors added algebraically?
question_answer2) State the essential condition for the addition of vectors.
question_answer3) Is time a vector quantity? Give reason.
question_answer4) Is pressure a vector? Give reason.
question_answer5) Can two vectors of different magnitudes be combined to give zero resultant?
question_answer6) When is the magnitude of the resultant of two vectors equal to either of them?
question_answer7) Are the magnitude and direction of \[(\vec{A}-\vec{B})\] same as that of\[(\vec{B}-\vec{A})\]?
question_answer8) Can\[\mathbf{\vec{A}+\vec{B}}=\mathbf{\vec{A}-\vec{B}}\] ?
question_answer9) When is the magnitude of \[(\vec{A}+\vec{B})\] equal to the magnitude of \[(\vec{A}-\vec{B})\] ?
question_answer10) Under what condition will the directions of sum and difference of two vectors be same?
question_answer11) If\[\vec{A}+\vec{B}=\vec{B}+\vec{A},\] what can you say about the angle between \[\vec{A}\] and \[\vec{B}\]?
question_answer12) Can we add a velocity vector to a displacement vector?
question_answer13) What is the minimum number of coplanar vectors of different magnitudes which can give zero resultant?
question_answer14) If\[\vec{a}+\vec{b}=\vec{c}\] and\[|\vec{a}|+|\vec{b}|=|\vec{c}|,\] what can we say about the direction of these vectors?
question_answer15) What is the resultant of vector\[\vec{A}\] multiplied by real number m?
question_answer16) Can a vector be multiplied by both dimensional and non-dimensional scalars?
question_answer17) What is the maximum number of components into which a vector can be resolved?
question_answer18) Can the magnitude of the rectangular component of a vector be greater than the magnitude of that vector?
question_answer19) Can a vector be zero when one of the components is not zero while all the other components are zero?
question_answer20) Can the increment \[\Delta a\] in the magnitude of vector \[\vec{a}\] be greater than the modulus of the increment of the vector, that is, \[|\Delta \vec{a}|\]? Can they be equal?
question_answer21) The direction of vector \[\vec{a}\] is reversed. Find \[\Delta \vec{a},|\Delta \vec{a}|\]and \[\Delta a\].
question_answer22) If \[\vec{a}\] and \[\Delta \vec{a}\] are directed opposite to each other, what is the relation between \[\Delta a\] and \[|\Delta \vec{a}|\]?
question_answer23) A vector \[\vec{a}\] is turned through a small angle \[d\theta \] without a change in its length. What are \[|\Delta \vec{a}|\] and \[\Delta a\]?
question_answer24) Give two conditions necessary for a given quantity to be a vector.
question_answer25) Is finite rotation a vector?
question_answer26) Can the scalar product of two vectors be negative?
question_answer27) What is the dot product of two per- perpendicular vectors \[\vec{A}\] and \[\vec{B}\]?
question_answer28) What is the dot product of two similar unit vectors?
question_answer29) What is the dot product of two dissimilar unit vectors? Or Calculate the value of \[\hat{i}.\hat{j}\].
question_answer30) If \[\vec{A}.\vec{B}=\vec{A}.\vec{C},\]is it correct to conclude that \[\vec{B}=\vec{C}\]?
question_answer31) If \[\vec{A},\vec{B}\] and \[\vec{C}\] are non-zero vectors and \[\vec{A}.\vec{B}=0\] and \[\vec{B}.\vec{C}=0,\] then find out the value of \[\vec{A}.\vec{C}\].
question_answer32) What is the magnitude and direction of\[\hat{i}+\hat{j}\]
question_answer33) What is the angle made by vector \[\vec{A}=2\hat{i}+2\hat{j}\]\[x\]-axis?
question_answer34) What should be the angle \[\theta \] between two vectors \[\vec{A}\] and \[\vec{B}\] for their resultant \[\vec{R}\] to be maximum?
question_answer35) What should be the angle \[\theta \] between two vectors \[\vec{A}\] and \[\vec{B}\] for their resultant \[\vec{R}\] to be minimum?
question_answer36) What is the effect on the magnitude of the resultant of two vectors when the angle \[\theta \] between them is increased from \[\mathbf{0}{}^\circ \] to\[\mathbf{180}{}^\circ \]?
question_answer37) Two persons are pulling the ends of string in such a way that the string is stretched horizontally. When a weight of \[\mathbf{10}\text{ }\mathbf{kg}\] is suspended in the middle of the string, the string does not remain horizontal. Can the persons make it horizontal again by putting it with a greater force?
question_answer38) What is the vector sum of \[n\] coplanar forces, each of magnitude F, if each force makes an angle of \[2\pi /n\] with the preceding force?
question_answer39) Two vectors \[\vec{A}\] and \[\vec{B}\] are in the same plane and angle between them is \[\theta \]. What is the magnitude and direction of \[\vec{A}\times \vec{B}\] ?
question_answer40) If \[\vec{A}\] and \[\vec{B}\] are two length vectors, then what is the geometrical significance of\[|\vec{A}\times \vec{B}|\]?
question_answer41) What is the unit vector perpendicular to the plane of vectors \[\vec{A}\] and \[\vec{B}\]?
question_answer42) What is the value of \[\vec{A}\times \vec{A}\]?
question_answer43) What is-the condition for two vectors to be collinear?
question_answer44) If \[\vec{A}\times \vec{B}=\vec{C}\times \vec{B},\] show that \[\vec{C}\] need not be equal to \[\vec{A}\] .
question_answer45) Find the value of \[\hat{i}\times \hat{j}.\]
question_answer46) What is \[\hat{i}.(\hat{j}\times \hat{k})\] ?
question_answer47) Under what condition will the equality: \[|\vec{A}\times \vec{B}|=\vec{A}.\vec{B}\] hold good?
question_answer48) What is the angle between \[(\vec{A}+\vec{B})\] and \[(\vec{A}\times \vec{B})\]?
question_answer49) Can there be motion in two dimensions with an acceleration only in one dimension?
question_answer50) Can the direction of velocity of a body change when the acceleration is constant?
question_answer51) Is the rocket in flight an example of projectile?
question_answer52) A stone is thrown vertically upwards and then it returns to the thrower. Is it a projectile?
question_answer53) Why does a projectile fired along the horizontal not follow a straight line path?
question_answer54) A body projected horizontally moves with the same horizontal velocity although it is under the action of force of gravity. Why?
question_answer55) What is the angle between the direction of velocity and acceleration at the highest point of a projectile path?
question_answer56) A bullet is dropped from a certain height and at the same time, another bullet is fired horizontally from the same height. Which one will hit the ground earlier and why?
question_answer57) A stone dropped from the window of a stationary bus takes 5 seconds to reach the ground. In what time the stone will reach the ground when the bus is moving with (a) constant velocity of \[80\text{km}{{\text{h}}^{-1}}\] (b) constant acceleration of\[2\text{km}{{\text{h}}^{-2}}\] ?
question_answer58) A bomb thrown as projectile explodes in mid-air. What is the path traced by the centre of mass of the fragments assuming the friction to be negligible?
question_answer59) At what point in its trajectory does a projectile have its (i) minimum speed (ii) maximum speed?
question_answer60) What will be the effect on horizontal range of a projectile when its initial velocity is doubled, keeping the angle of projection same?
question_answer61) A projectile is fired at an angle of \[\mathbf{15}{}^\circ \] to the horizontal with the speed \[\upsilon \]. If another projectile is projected with the same speed, then at what angle with the horizontal it must be projected so as to have the same range?
question_answer62) Is the maximum height attained by projectile is largest when its horizontal range is maximum?
question_answer63) What will be the effect on maximum height of a projectile when its angle of projection is changed from \[\mathbf{30}{}^\circ \] to\[\mathbf{60}{}^\circ \], keeping the same initial velocity of projection?
question_answer64) A body is projected with speed \[u\] at an angle \[\theta \] to the horizontal to have maximum range. What is the velocity at the highest point?
question_answer65) What is the angle of projection for a projectile motion whose range R is n times the maximum height H?
question_answer66) The greatest height to which a man can throw a stone is h. What will be the greatest distance up to which he can throw the stone?
question_answer67) A particle is projected at an angle \[\theta \] from the horizontal with kinetic energy K. What is the kinetic energy of the particle at the highest point?
question_answer68) A man can jump on the moon six times as high as on the earth. Why?
question_answer69) A projectile of mass m is fired with velocity \[\upsilon \] at an angle \[\theta \] with the horizontal. What is the change in momentum as it rises to the highest point of the trajectory?
question_answer70) A projectile of mass m is thrown with velocity \[\upsilon \] from the ground at an angle of \[\mathbf{45}{}^\circ \] with the horizontal. What is the magnitude of change in momentum between leaving and arriving back at the ground?
question_answer71) A block slides down a smooth inclined plane when released from the top while another falls freely from the same point. Which one of them will strike the ground earlier?
question_answer72) Why does a tennis ball bounce higher on hills than in plains?
question_answer73) Two projectiles A and B are projectiles with velocities \[\sqrt{2\upsilon }\]and \[\upsilon \] respectively. They have the same range. If A is thrown at angle of \[\mathbf{15}{}^\circ \] with the horizontal, then what is the angle of projection of B?
question_answer74) A stone is thrown horizontally with a speed \[\sqrt{2gh}\] from the top of a wall of height h. It strikes the level ground through the foot of the wall at a distance \[x\] from the wall. What is the value of \[x\]?
question_answer75) The velocity of a particle is constant in magnitude but not in direction. What is the nature of trajectory?
question_answer76) What is the angle between velocity vector and acceleration vector in uniform circular motion?
question_answer77) For uniform circular motion, does the direction of centripetal acceleration depend upon the sense of rotation?
question_answer78) If both the speed and radius of the circular path of a body are doubled, how will the centripetal acceleration change?
question_answer79) A stone tied to the end of a string is whirled in a circle. If the string breaks, the stone flies away tangentially. Why?
question_answer80) When a knife is sharpened with the help of a rotating grinding stone, the spark always travels tangentially to it. Why?
question_answer81) Which of the following quantities are independent of the choice of orientation of the coordinate axes : \[\vec{a}+\vec{b},3{{a}_{x}}+2{{b}_{y}},|\vec{a}+\vec{b}-\vec{c}|,\] angle between \[\vec{b}\] and \[\vec{c},\lambda \vec{a}\],where \[\lambda \] is a scalar?
question_answer82) Do \[\vec{a}+\vec{b}\] and \[\vec{a}-\vec{b}\] lie in the same plane. Give reason.
question_answer83) Can we apply the commutative and associative laws to vector subtraction also?
question_answer84) Can three vectors not in one plane give a zero resultant? Can four vectors do so?
question_answer85) What is the difference between the following two data : (i) 8 (5 km/hr, east) (ii) (8 hr) (5 km/hr, east)?
question_answer86) Is \[|\vec{a}+\vec{b}|\] greater than or less than \[|\vec{a}|+|\vec{b}|\]? Give reason.
question_answer87) Is \[|\vec{a}-\vec{b}|\] greater than or less than \[|\vec{a}|+|\vec{b}|\]?
question_answer88) Under what condition does the equality: \[|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|\] hold good?
question_answer89) The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.
question_answer90) Find the conditions for two vectors to be (i) parallel and (ii) perpendicular to each other.
question_answer91) The resultant of two vectors \[\vec{P}\] and \[\vec{Q}\] is perpendicular to \[\vec{P}\] and its magnitude is half that of \[\vec{Q}\]. What is the angle between \[\vec{P}\] and \[\vec{Q}\]?
question_answer92) The magnitude of vector \[\vec{A}\] is 2.5 metre and is directed towards east. What will be the magnitudes and directions of the following : (a) \[-\vec{A}\] (b) \[\vec{A}/2\] (c) \[2.5\vec{A}\] (d) \[4\vec{A}\]?
question_answer93) A person sitting in a moving train throws a ball vertically upwards. How will the ball appear to move to an observer (i) sitting inside the train (ii) standing outside the train? Give reason.
question_answer94) A bob hung from the celling of a room by a string is performing simple harmonic oscillations. What will be the trajectory of the bob, if the string is cut, when bob is (i) at one of its extreme positions, (ii) at its mean position?
question_answer95) Prove that the horizontal range is same when angle of projection is (i) greater than \[\mathbf{45}{}^\circ \] by certain value and (ii) less than \[\mathbf{45}{}^\circ \] by the same value.
question_answer96) Two bombs of 5 kg and 10 kg are thrown from a cannon with the same velocity in the same direction, (i) Which bomb will reach the ground first? (ii) If the bombs are thrown in the same direction with different velocity, what would be the effect?
question_answer97) Two bodies are thrown with the same initial velocity at angles \[\alpha \] and \[\left( \mathbf{90}{}^\circ \text{ }-\text{ }\alpha \right)\] with the horizontal. What will be the ratio of (i) maximum heights attained by them and (ii) their horizontal ranges?
question_answer98) At which points on the projectile trajectory is the (i) potential energy maximum (ii) kinetic energy minimum and (iii) total energy maximum?
question_answer99) A body A of mass m is thrown with velocity \[\upsilon \] at an angle \[\mathbf{30}{}^\circ \] to the horizontal and another body B of the same mass is thrown with velocity \[\upsilon \] at an angle of \[\mathbf{60}{}^\circ \] to the horizontal, find the ratio of the horizontal range and maximum height of A and B.
question_answer100) A ball of mass m is thrown vertically up. Another ball of mass 2m is thrown at an angle \[\theta \] with the vertical. Both of them remain in air for the same period of time. What is the ratio of the heights attained by the two balls?
question_answer101) A skilled gunman always keeps his gun slightly tilted above the line of sight while shooting. Why?
question_answer102) Is it important in the long jump that how much height you take for jumping? What factors determine the span of a jump?
question_answer103) A body is thrown horizontally with a velocity \[\upsilon \] from a tower of height H. After how much time and at what distance from the base of the tower will the body strike the ground?
question_answer104) A ball is thrown horizontally and at the same time another ball is dropped down from the top of a tower (i) will both the balls reach the ground at the time? (ii) Will both strike the ground with the same velocity?
question_answer105) A horizontal stream of water leaves an opening in the side of a tank. If the opening is h metre above the ground and the stream hits the ground D metre away, then what is the speed of water as it leaves the tank in terms of g, h and D?
question_answer106) A railway carriage moves over a straight, track with acceleration a. A passenger in the carriage drops a stone. What is the acceleration of the stone w. r. t. the carriage and the earth?
question_answer107) A glass marble slides from rest from the topmost point of a vertical circle of radius r along a smooth chord. Does the time of descent depend upon the chord chosen?
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