A body is projected with a speed $u \mathrm{~ms}^{-1}$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $(3 / 4)$ th of the initial kinetic energy. The value of $\beta$ is

A force of $ F=0.5 \mathrm{~N} $ is applied on lower block as shown in figure. The work done by lower block on upper block for a displacement of 3 m of the upper block with respect to ground is (Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ )

A pendulum of mass 1 kg and length $ l=1 \mathrm{~m} $ is released from rest at angle $ \theta=60^{\circ} $. The power delivered by all the forces acting on the bob at angle $ \theta=30^{\circ} $ will be (Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ )

An ideal massless spring $ S $ can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at $ 30^{\circ} $ to the horizontal. A 10 kg block $ M $ is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2 m . If $ g=10 \mathrm{~m} / \mathrm{s}^{2} $, what is the speed of mass just before it touches the spring?