A small coin of mass $80g$ is placed on the horizontal surface of a rotating disc. The disc starts from rest and is given a constant angular acceleration $\alpha =2rad/s^2.$ The coefficient of static friction between the coin and the disc is ${\mu }_s=3/4$ and cofficient of kinetic friction is ${\mu }_k=0.5.$ The coin is placed at a distance $r=1m$ from the centre of the disc. The magnitude of the resultant force on the coin exerted by the disc just before it starts slipping on the disc is

A box is placed on the floor of a truck moving with an acceleration of $7m{s}^2.If$ the coeffecient of kenetic friction between the box and surface of the truck is $0.5,find$ the acceleration of the box relative to the truck

A mass 1kg attached to the end of a flexible rope of diameter $d=0.25mis$ raised vertically by winding the rope on a reel as shown. If the reel is turned uniformly at the rate of $2r.p.s.$ What is the tension in rope. The inertia of rope may be neglected.

Three masses of $16kg,8kg$ and $4kg$ are placed in contact as shown in Figure. If a force of $140N$ is applied on $4kg$ mass, then the force on $16kg$ will be

A heavy uniform chain lies on horizantal table top. If the coefficient of friction between the chain and the table surface is $0.5$, the maximum percentage of the length of the chain that can hang over one edge of the table is

A coin, placed on a rotating turntable slips, when it is placed at a distance of $9cm$ from the center. If the angular velocity of the turnable is tripled, it will just slip, If its distance from the center is

A particle is projected horizontally from the top of a tower with a velocity $v_0.$ If v be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directely proportional to