0
question_answer1) A rigid body can be hinged about any point on the x-axis. When it is hinged such that the hinge is at x, the moment of inertia is given by\[I=2{{x}^{2}}-12x+27\]. Find the \[x\] coordinate of centre of mass.
question_answer2) A uniform ladder of mass 10 kg leans against smooth vertical wall making an angle \[53{}^\circ \]with it. The other end rests on rough horizontal floor. Find the friction coefficient just necessary for ladder to be at rest is approximately.
question_answer3) The two ends A and B of a uniform of length \[\ell =1m\] and mass m are moving with velocities \[{{V}_{A}}\]and \[{{V}_{B}}\]as shown. The length AP, where P is point on the rod with velocity 12 m/s, is 8 K cm. Find the value of K.
question_answer4) A uniform disc of mass M and radius R is hanging from a rigid support and is free to rotate about a horizontal axis passing through its center in vertical plane as shown. A particle of mass m falls vertically and hits the disc (at a point at horizontal diameter) with a velocity \[{{v}_{0}}\](in m/s) and sticks to it. The disc just completes the vertical circular motion afterwards. Find \[{{v}_{0}}\] (in m/s) \[\left( M=7\text{ }kg,\text{ }m=1\text{ }kg,\text{ }R=10\text{ }cm \right).\]
question_answer5) On the rod on B point a force \[\vec{F}=3\hat{i}+10\hat{j}+5\hat{k}\]is applied then the ratio of torque about point A and about y- axis is \[\sqrt{n}\] then the value of n is?
question_answer6) A disc of mass M & radius R is placed a rough horizontal surface with its axis horizontal. A light rod of length '2R' is fixed to the disc at point 'A' as shown in figure and a force \[\frac{3}{2}\]Mg is applied at the other end. If disc starts to roll without slipping find the value of \[''10\times {{\mu }_{\min }}''\]where \[{{\mu }_{\min }}\] is minimum coefficient of friction b/w disc & horizontal surface required for pure rolling-
question_answer7) A homogeneous rod of mass 3 kg is pushed along smooth horizontal surface by a horizontal force F=40 N. the angle \['\theta '\](in degree) for which rod has pure translation motion. Then the value of \[\left( \theta -30{}^\circ \right)\] \[\left( g=10m/{{s}^{2}} \right)\]-
question_answer8) Uniform rod AB is hinged at end A in horizontal position as shown in the figure. The other end is connected to a block through a massless string as shown. The pulley is smooth and massless. Mass of block and rod is same and is equal to m. Then acceleration of block just after release from this position is\[\frac{3g}{n}\]. Find n.
question_answer9) A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance \[\ell \] from the cylinder holds on end of the string and pulls the cylinder towards him as shown in figure. There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is\[n\times \ell \]. Find n.
question_answer10) Just after release of rod (as shown) on smooth horizontal track. Find the ratio\[\left( \frac{2a}{\ell a} \right)\], where \[a\] is acceleration of point A and \[\alpha \] is angular acceleration of rod just after release
question_answer11) The figure shown is just before collision, the velocity of centre of uniform disc is \[{{v}_{0}}\]vertically downward & \[{{\omega }_{0}}\]is the angular velocity as shown. If is found that collision is elastic and after collision disc stops rotating then if coefficient of friction is \[\left( \frac{1}{P} \right)\]then the value of P is? If\[{{v}_{0}}={{R}_{\omega 0}}\]. (R is radius of disc)
question_answer12) A solid cylinder of mass M and radius 2R is rolled up on a incline with help of a plank of mass 2M as shown in Fig. A constant force F is acting on the plank parallel to incline. There is no slipping at any of the contact. The force of friction between the plank and cylinder is given by. \[\frac{N\times F+2mg\sin \theta }{19}\]. Find N.
question_answer13) A uniform stick of mass m and length ℓ with \[I=\frac{1}{12}\]\[m{{\ell }^{2}}\]spins around on a frictionless horizontal plane, with its CM stationary. A mass M is placed on the plane, and the stick collides elastically with it, as shown (with the contact point being the end of the stick). What should be the ratio of \[\frac{m}{M}\]be so that after the collision the stick has translational motion, but no rotational motion?
question_answer14) A disc of mass m and radius R is placed over a plank of same mass m. There is sufficient friction between the disc and the plank to prevent slipping. A force F is applied at the centre of the disc. Then, the acceleration of the plank is \[\frac{F}{Km}\]. Find the value of K.
question_answer15) A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity\[v=a+b{{t}^{2}}\]. If the cylinder is not allowed to slip, the time when the cylinder is about to topple is \[n\times \frac{gr}{8bh}\] where n is equal to.
Please Wait you are being redirected....
You need to login to perform this action.You will be redirected in 3 sec
OTP has been sent to your mobile number and is valid for one hour
Your mobile number is verified.
A constant force F is acting on the plank parallel to incline. There is no slipping at any of the contact. The force of friction between the plank and cylinder is given by. \[\frac{N\times F+2mg\sin \theta }{19}\]. Find N. 
