A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :
An insect is at the bottom of a hemisphere ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height 'h' from the bottom. If the coefficient of friction b/w the ground and insect is 0.75. Then h is :
A mass of 10 kg is suspended by a rope of length 4m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of with the vertical. Then F (in newtons) equals: (Take and the rope to be massless):