A small ball is connected to a block by a light string of length l. Both are initially on the ground. There is sufficient friction on the ground to prevent the block from slipping. The ball is projected vertically up with a velocity u, where `2gl lt u^(2) lt 3gl`. The centre of mass of the block + ball' system is C.

A helicopter is rising vertically up with a velocity of 5 ms^( –1) . A ball is projected vertically up from the helicopter with a velocity V (relative to the ground). The ball crosses the helicopter 3 second after its projection. Find V.

A small ball B of mass m is suspended with light inelastic string of length L from a block A of same mass in which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle theta from equilibrium position and then released. The displacement of centre of mass of A + B system till the string becomes vertical is

A small ball B of mass m is suspended with light inelastic string of length L from a block A of same mass in which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle theta from equilibrium position and then released. The displacement of centre of mass of A + B system till the string becomes vertical is

A small block of mass m is projected on a larger block of mass 10 m and length l with a velocity v as shown in the figure. The coefficient of friction between the two block is mu_(2) while that between the lower block and the ground is mu_(1) . Given that mu_(2) gt 11 mu_(1) . (a) Find the minimum value of v , such that the mass m falls off the block of mass 10 m . (b) If v has minimum value, find the time taken by block m to do so.

A small block of mass m is projected on a larger block of mass 10 m and length l with a velocity v as shown in the figure. The coefficient of friction between the two block is mu_(2) while that between the lower block and the ground is mu_(1) . Given that mu_(2) gt 11 mu_(1) . (a) Find the minimum value of v , such that the mass m falls off the block of mass 10 m . (b) If v has minimum value, find the time taken by block m to do so.

Two blocks of masses 1 kg and 2 kg are joined by a massless inextensible string of length 3m. Both blocks are kept on a horizontal table as shown. Friction coefficient between 2 kg block and table is zero. They are rotated about a vertical axis passing at a distance of 1m from 1 kg. Force of friction on 1kg block is (assume that there is enough friction between 1 kg block ground)

Two blocks of masses 1 kg and 2 kg are joined by a massless inextensible string of length 3m. Both blocks are kept on a horizontal table as shown. Friction coefficient between 2 kg block and table is zero. They are rotated about a vertical axis passing at a distance of 1m from 1 kg. Force of friction on 1kg block is (assume that there is enough friction between 1 kg block ground)

A ball is thrown vertically upward with a velocity u from the top of a tower. If it strikes the ground with velocity 3u, the time taken by the ball to reach the ground is