A ball of mass $m$ moving with speed $u$ collides with a smooth horizontal surface at angle $\theta$ with it as shown in figure. The magnitude of impulse imparted to surface by ball is [Coefficient of restitution of collision is $e$]
A ball of mass $m$ moving with speed $u$ collides with a smooth horizontal surface at angle $\theta$ with it as shown in figure. The magnitude of impulse imparted to surface by ball is [Coefficient of restitution of collision is $e$]
- A
$m u(1+e) \cos \theta$
- B
$m u(1-e) \sin \theta$
- C
$m u(1-e) \cos \theta$
- D
$m u(1+e) \sin \theta$
Similar Questions
A small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L _0$ the particle speed is $v = v _0$. The piston is moved inward at a very low speed $V$ such that $V \ll \frac{ dL }{ L } v _0$, where $dL$ is the infinitly small displacement of the piston. Which of the following statement($s$) is/are correct?
$(1)$ The rate at which the particle strikes the piston is $v / L$
$(2)$ After each collision with the piston, the particle speed increases by $2 V$
$(3)$ The particle's kinetic energy increases by a factor of $4$ when the piston is moved inward from $L _0$ to $\frac{1}{2} L _0$
$(4)$ If the piston moves inward by $d L$, the particle speed increases by $2 v \frac{d L}{L}$
A small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L _0$ the particle speed is $v = v _0$. The piston is moved inward at a very low speed $V$ such that $V \ll \frac{ dL }{ L } v _0$, where $dL$ is the infinitly small displacement of the piston. Which of the following statement($s$) is/are correct?
$(1)$ The rate at which the particle strikes the piston is $v / L$
$(2)$ After each collision with the piston, the particle speed increases by $2 V$
$(3)$ The particle's kinetic energy increases by a factor of $4$ when the piston is moved inward from $L _0$ to $\frac{1}{2} L _0$
$(4)$ If the piston moves inward by $d L$, the particle speed increases by $2 v \frac{d L}{L}$
- [IIT 2019]
Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. The ratio of the height attained by $A$ and $B$ after collision will be: (neglect friction)
Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. The ratio of the height attained by $A$ and $B$ after collision will be: (neglect friction)
A ball hits a vertical wall horizontally at $10m/s$ bounces back at $10 m/s$
A ball hits a vertical wall horizontally at $10m/s$ bounces back at $10 m/s$
A ball is projected vertically down with an initial velocity from a height of $ 20 m$ onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$
A ball is projected vertically down with an initial velocity from a height of $ 20 m$ onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$
A ball of mass $10\, kg$ is moving with a velocity of $10\, m/s$. It strikes another ball of mass $5\, kg $ which is moving in the same direction with a velocity of $4 \,m/s$. If the collision is elastic, their velocities after the collision will be, respectively
A ball of mass $10\, kg$ is moving with a velocity of $10\, m/s$. It strikes another ball of mass $5\, kg $ which is moving in the same direction with a velocity of $4 \,m/s$. If the collision is elastic, their velocities after the collision will be, respectively