An inclined plane wound into a spiral around a straight rod

A spool of mass M and radius 2R lies on an inclined plane as shown in the figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass m . The value of m so that system is in equilibrium is

A uniform rod AB of length l and mass m hangs from point A in a car moving with velocity v_(0) on an inclined plane as shown in Fig. The rod can rotate in vertical plane about the axis at point A . if the car suddenly stops, the angular speed with which the rod starts rotating is

A semicircular rods is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the straight rod in a given time.

An inclined plane makes an angle of 60^(@) with horizontal. A disc rolling down this inclined plane without slipping has a linear acceleration equal to

In Fig. a coil of single turn is wound on a sphere of radius r and mass m. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equilibrium, the value of B is [Current in the coil is i]

The upper half of an inclined plane with an angle of inclination theta, is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is

A hollow sphere is released from top of an inclined plane of inclination 30º and length of inclined plane is /. If sphere rolls without slipping then its speed at bottom is

A particle is projected on an inclined plane with a speed u as shown in (Fig. 5.61). Find the range of the particle on the inclined plane. .

A block is kept on a smooth inclined plane of angle of inclination theta that moves wuth a contact acceleration so that the block does not slide relative to the inclined plane. If the inclined plane stops the normal contact force offered by the plane on the block changes by a factor

A block of mass m takes time t to slide down on a smooth inclined plane of angle of inclination theta and height h. If same block slids down on a rough inclined plane of same angle of inclination and same height and takes time n times of initial value, then coefficient friction between block and inclined plane is