A bob of mass $\mathrm{M}$ is suspended by a massless string of length $\mathrm{L}$. The horizontal velocity $\mathrm{V}$ at position $\mathrm{A}$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies Figure:
$\theta=\frac{\pi}{4}$
$\frac{\pi}{4}<\theta<\frac{\pi}{2}$
$\frac{\pi}{2}<\theta<\frac{3 \pi}{4}$
$\frac{3 \pi}{4}<\theta<\pi$
A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. $\mathrm{km}$
A particle of mass m moving with velocity ${V_0}$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be
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 $6\, kg$ is ............ $\mathrm{J}$
A ball is thrown from $10\,m$ height at speed $v_0$ vertically downward. In colliding surface of earth it looses $50\%$ of its energy and again reach upto same height. Value of $v_0$ is :- .................$\mathrm{m}/ \mathrm{s}$
A bomb of mass $12\,\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3.$ The $K.E.$ of the smaller fragment is $216\,\,J.$ The momentulm of heavier fragment is (in $kg-m/sec$ )