In a colony of 100 blocks of flats numbering 1 to 100, a school van stops at every sixth block while a school bus stops at every tenth block. On which stops will both of them stop if they start from the entrance of the colony?

A 100 kg block is started with a speed of 2.0 m s^(-1) on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20. (a) calculate the change in the internal energy of the block=-belt system as the block comes to a stop on the belt. (b) consider the sutuation from a frame of reference moving at 2.0 m s^(-1) along the initial velocity of the block. as seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at 2.0 m s^(-1) , calculate the increase in the kinetic energy of the block as it stops slipping past the belt. (c ) find the work done in this frame by the external force holding the belt.

A block of mass 100 g is moved with a speed of 5(m)//(s) at the highest point in a closed circular tube of radius 10 cm kept in a vertical plane. The cross-section of the tube is such that the block jst fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. The work done by the tube on the block during the process will be

Asseration : A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a ceratin distance. The surface is now tilted to an angle of 30^@ with the horizontal and same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is small than the first situation. Reason : The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

In the figure shown upper block is given a velocity of 6 m//s and lower block 3 m//s . When relative motion between them is stopped. .

A knife of mass m is at a height x from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating - distance y. The work done y the wooden block to stop the knife is

A plank of mass 5 kg in kept on a smooth surface. A block of 1 kg is kept on it and is given a velcoity of 12 m/s. There is friction between the block and the plank. Assuming the plank to be very long, find the magnitude of work done (in Joules) by friction on block till the relative sliding between them stops.