Rotation Questions and Answers

Answer all questions Each carries 4 mark 5 A rotational K E of a particle rotating about a certain axis is 16J Calculat the angular moment of the particle about the same axis of rotation if the M I about its axis of rotation is 2 Kg m 2

M I about its axis of rotation is 2 Kg m 2 7 Calculate the MI of a cylinder of length 2 m radius 5 cm and density 8 x 10 3 Kg m 3 about its a axis of the cylinder b axis passing through the centre and perpendicular to its length

A dise weight W 100N and radius r 0 25 m supported at it acted up on by a constant couple of moment 6 Nm and a force of 50 N is applied to a cord wrapped around its periphery The angular velocity in rad s at two seconds after starting from rest is 5 Nm B 50 N

At a point beats frequency of n Hz is observed It means 1 medium particles at that point are vibrating with frequency n Hz 2 amplitude of vibrations changes simple harmonically with frequency n Hz at that point only 3 at that point zero intensity is observed 2n times per second 4 none of the above

a The diagram given below shows a uniform meter rule of weight 100 gf being balanced c a knife edge placed at the 40 cm mark by suspending a weight w gf at the mark 20 cr find 0 20 w gf 40 a 100 cm Metre rule to i the value of w ii the resultant moment and its direction if the weight w is moved to the mark 30 cm iii the position of another weight of 50 of to balance the rule in part ii

As shown in the figure two balls of same mass m are situated at the centre of a tube of mass M and are rotating with a uniform angular velocity 0 If the balls suddenly come to end of the tube the resultant angular velocity will be O M M 3m M M 6m O M 6m M 000 wh WO 1o 30 1 2 1 2 Marks 4 1

QA thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity w Another disc of the same dimension but of mass M 4 is placed gently on the first disc coaxially Find the angular velocity of the system

A weightless rod of length 2 carries two equal masses m one tied at lower end A and the other at the middle of the rod at B The rod can rotate vertical plane about a fixed horizontal axis passing through C The rod is released from rest in horizontal axis passing through C The rod is released from rest in horizontal position The speed of the mass B at the instant rod becomes vertical is O O A C 1 BOm 3gl 1 m

QA uniform rod of mass m and length I is free to rotate in the vertical plane about a horizontal axis passing through its end The rod is released from rest in the position shown by slightly displacing it clockwise Find the hinge reaction at the axis of rotation at the instant the rod tums through T

QA thin rod MN free to rotate in the vertical plane about the fixed end N is held horizontal When the end M is released the speed of this end when the rod makes an angle a with the horizontal will be proportional to see figure M N A B C D COS a COS a sin a a

A mobile system in the equilibrium condition is shown what is the ratio between weight of square and circle TA HII A 1 6 B 3 1 C 3 4 D 6 1 E 10 1 3cm 6 cm 4cm 1cm

A slender homogeneous rod of length 2L floats partly immersed in water being supported by a string fastened to one of its ends as shown in the figure The specific gravity of the rod is 0 36 The length of the rod that extends out of the water is KL Find the value of K 10

Two identical circular discs A and Beach of mass m and radius R are placed horizontally on a smooth horizontal surface with their centers fixed to the surface and touching each other as shown Now an impulse P is applied to the disc A as shown If there is no slipping between the discs the angular velocity of each disc will be

position so that it rotates about A in vertical plane Which of the following represents the hinge force when rod becomes horizontal Rod is rotating clockwise Br

A particle of mass m is thrown with speed vo at an angle 30 with horizontal The angular momentum about the point of projection when the particle is at the highest point of its trajectory Question Type Single Correct Type 1 3mv 2g

radius R is rolling on a horizontal surface Find the angular momentum of the disc about an axis perpendicular to the plane of disc and fixed at point P to the disc P R 2 V