$A$ mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is

$A$ body thrown vertically upwards from the ground reaches a maximum height $h$. The ratio of the kinetic and potential energies of the body at a height $40 \%$ of $h$ from the ground is

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?

$A$ body of mass $5 \,kg$ is thrown vertically up with a kinetic energy of $490 \,J$. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8 \,ms^{-2}$) (in $\,m$)

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x$ such that $\frac{\mu mg}{K} < x < \frac{2\mu mg}{K}$,and then released. Which of the following laws/principles of physics can be applied to the spring-block system?

$A$ ball of mass $20 \ kg$ is at rest on a hill of height $100 \ m$. It starts rolling down,reaches the ground,climbs another hill of height $30 \ m$,and finally rolls down to a horizontal platform at a height of $20 \ m$ from the ground. What will be its velocity at this point? (Assume $g = 10 \ m/s^2$)