A bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is
$\sqrt {\frac{M}{{M + m}}} v$
$\sqrt {\frac{m}{{M + m}}} v$
$\frac{m}{{M + m}}v$
$\frac {v}{2}$
Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $W$. Here $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$. The velocity of particle at time $t = 2\, sec$. will be ........... $\mathrm{m}/ \mathrm{s}$
A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is
State if each of the following statements is true or false. Give reasons for your answer.
$(a)$ In an elastic collision of two bodies, the momentum and energy of each body is conserved.
$(b)$ Total energy of a system is always conserved, no matter what internal and external forces on the body are present.
$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.
$(d)$ In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.
If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)
A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are