A $\sqrt[]{34}m$ long ladder weighing 10kg leans on a frictionless wall. Its feet rest on the floor 3m away from the wall as shown in the figure. If F_f and F_w are the reaction forces of the floor and the wall, then ratio of F_w / F_f will be:

(Use g = 10 m/s²)

 

A ball is spun with angular acceleration a = 6t² – 2t where t is in second and a is in rads^-1. At t = 0, the ball has angular velocity of 10 rads^-1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

A set of 20 tuning forks is arranged in series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ___________Hz.

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is-

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

A spherical of 1 kg mass and radius R is rolling with angular speed <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\omega$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is $\frac{a}{3}{R}^2\omega .$ <!-- [if gte mso 9]><xml> </xml><![endif]--> The value of a will be: