A body of mass $2\, kg$ is thrown up vertically with K.E. of $490$  joules. If the acceleration due to gravity is $9.8$$m/{s^2}$, then the height at which the K.E. of the body becomes half its original value is given by ............ $\mathrm{m}$

Two identical uniform discs roll without slipping on two different surfaces $AB$ and $CD$ (see figure) starting at $A$ and $C$ with linear speeds $v _1$ and $v _2$, respectively, and always remain in contact with the surfaces. If they reach $B$ and $D$ with the same linear speed and $v_1=3 \ m / s$, then $v_2$ in $m / s$ is $\left(g=10 \ m / s ^2\right)$

The graph between $E$ and $v$ is

If the linear momentum is increased by $5\%$, the kinetic energy will increase by.......$\%$

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be $...\%$

The momentum of a body is increased by $50 \%$. The percentage increase in the kinetic energy of the body is $...........\,\%$