The upper half of an inclined plane with inclination `theta` is perfectly smooth, while the lower half is rough. A bdy starting from rest at the top will again come to rest at the bottom, find the coefficient of friction for the lower half.

When a body slides down from rest along a smooth inclined plane making anangle of 45^@ with the horizontal, it takes time T. when the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

An inclined plane making an angle of 30^@ with the horizontal is placed in a uniform horizontal electric of 100 V m^-1 as shown in the figure A particle of mass 1 kg and charge 0.01 C is allowed to slide down from rest from a height of 1 m. If the coefficient of frictio nis 0.2, find the time it will take the particle to reach the bottom.

A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined at an angle theta = 15^@ with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

A 1 kg block situated on a rough incline is connected to a spring of spring constant 100N m^-1 as shown in Fig. 6.17. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.

Two bodies of masses m_1 and m_2 are connected byh a ight string passing over a smooth light pulley fixed at the end of an inclined plane.the mass m_1 lies on the inclined plne nd m_2 bags vertically.The system is at rest.Find the angle of the inclination of the inclined plane and the force exerted by the inclined plane on the body of mass m_1 .

A car of mass 1000 kg starts from rest and comes down an inclined slope. If it travels a distance of 300 m in 30 seconds, calculate force acting on the bus

A rough incline plane is placed on a cart moving with a constnat velocity u on horizontal ground. A block of mass M rests on the incline. Is any work done by fore of friction between the block and incline? Is there then a dissipation of energy?

A body losses half of its velocity while penetrating 3 cm into a wooden block, then how much will it penetrate ore before coming to rest?

A car of mass 1000 kg starts from rest and comes down an inclined slope. If it travels a distance of 300 m in 30 seconds, calculate acceleration

A rectangular box lies on a rough incli ned surface. The co-efficient of friction between the surface and the box is mu. Let the mass of the box is be m. At what angle of inclination theta of the plane to the horizontal will the box just start to slide down the plane?