Somari sweeps 600 m long railway platform in `2 1/2` hours. His wife Imarati sweeps `2/3\ r d` of the same platform in `1 1/2\ hou r sdot` Who sweeps more speedily?

A man stands on a rotating platform with his arms stretched holding a 5 kg weight in each hand. The angular speed of the platform is 1.2 rev s^-1 . The moment of inertia of the man together with the platform may be taken to be constant and equal to 6 kg m^2 . If the man brings his arms close to his chest with the distance n each weight from the axis changing from 100 cm to 20 cm . The new angular speed of the platform is.

A point p moves in counter - clockwise direction on a circular path as shown in the figure . The movement of 'p' is such that it sweeps out in the figure . The movement of 'p' is such that it sweeps out a length s = t^(3) + 5 , where s is in metres and t is in seconds . The radius of the path is 20 m . The acceleration of 'P' when t = 2 s is nearly .

X takes 3 hours more than Y to walk 30km. But, if X double his pace, he is ahead of Y by 1 1/2hou r s . Find their speed of walking.

Two blocks of masses m_(1) and m_(2) are placed in contact with each other on a horizontal platform as shown in figure The coefficent of friction between m_(1) and platform is 2mu and that between block m_(2) and platform is mu .The platform moves with an acceleration a . The normal reation between the blocks is

A circular platform is mounted on a vertical frictionless axle. Its radius is r = 2 m and its moment of inertia I = 200 kg m^2 . It is initially at rest. A 70 kg man stands on the edge of the platform and begins to walk along the edge at speed v_0 = 1 m s^-1 relative to the ground. The angular velocity of the platform is: a) 1.2 rad/s b) 0.4 rad/s c) 0.7 rad/s d) 2 rad/s

A gun is fired from a moving platform and ranges of the shot are observed to be R_1 and R_2 when the platform is moving forwards and backwards, respectively, with velocity v_P . Find the elevation of the gun prop in terms of the given quantities.

A platform is moving upwards with a constant acceleration of 2 m s^-2 . At time t = 0 , a boy standing on the platform throws a ball upwards with a relative speed of 8 m s^-1 . At this instant, platform was at the height of 4 m from the ground and was moving with a speed of 2 m s^-1 . Take g = 0 m s^-2 . Find (a) when and where the ball strikes the platform. (b) the maximum height attained by the ball from the ground. ( c) the maximum distance of the ball from the platform.

A boy is standing on a platform which is free to rotate about its axis. The boy holds an open umbrella in his hand. The axis of the umbrella coincides with tht of the platform. The moment of inertias of the platform plus the boy sytem is 3.0xx10^-3 kg-m^ and that of the umbrella is 2.0xx10^-3 kg-m^2 . The boy starts spinning the umbrella ils 2.0xx10^-3 kg-m^2 . and that the umbrella is 2.0xx10^-3kg-m^2 . The boy starts of 2.0 rev/s with repsect to himself. Find the angular velocity imparted to the platform.

In a double star system one of mass m_(1) and another of mass m_(2) with a separation d rotate about their common centre of mass. Then rate of sweeps of area of star of mass m_(1) to star of mass m_(2) about their common centre of mass is

A square platform of side length 8m is is situated in x-z plane sucha that it is at 16 m form the x -axis and 8 m from the z -axis as shown in figure. A particle is projected with velocity overset(vec)(v)=(v_(2)overset(hat)(i)+25hat(j)) m//s relative to wind form origin and at the same instant the platform starts with acceleration overset(vec)=(2hat(i)+2.5hat(j)) m//s^(2) . Wind is blowing with velocity v_(1)hat(k).g=10m//s^(2) {:(,,"ListI",,"List II"),((P),,"Least possible values of " V_(2) "(in M/s) so that particle hits the platform or edge of platfrom is",,(1) 4),((Q),,"Least possible values of " v_(1) "(in m/s) so that particle hits the platform or edge or platform is ",,(2) 6),((Q),,"If t is the time (in seconds) after particle hits the platform then 2t is equal to ",,(3) 8),((S),,"Value of displacement with respect to ground (in m) of the particle in y-direction , when " v_(2) " has its minimum possible value is (till particle hits the platform or edge of platform)",,(4) 20):}