A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity to it at half of maximum height from ground is
$\frac{m g u \cos \theta}{\sqrt{2}}$
$\frac{m g u \sin \theta}{\sqrt{2}}$
$\frac{m g u \cos (90+\theta)}{\sqrt{2}}$
Both $(b)$ and $(c)$
A force $F = - K(yi + xj)$ (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point $(a, 0)$ and then parallel to the y-axis to the point $(a, a)$. The total work done by the force F on the particles is
A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of restitution then before coming to rest the total distance travelled during rebounds will be:-
If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ........... $\%$
A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is