A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement(s) related to particle $m$
A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement(s) related to particle $m$
- A
Its kinetic energy is $K_f = \left( {\frac{{mM}}{{m + M}}} \right)gh$
- B
$v_1 = v_0 \left( {\frac{{M - m}}{{M + m}}} \right)$
- C
The ratio of its final kinetic energy to its initial kinetic energy is $\frac{{{K_{\text{f}}}}}{{{K_i}}} = {\left( {\frac{M}{{m + M}}} \right)^2}$
- D
It moves opposite to its initial direction of motion
Similar Questions
$A$ small sphere is moving at $a$ constant speed in $a$ vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.
$I$ - kinetic energy
$II$- gravitational potential energy
$III$ - momentum
Which of these quantities will change as this sphere moves around the circle?
$A$ small sphere is moving at $a$ constant speed in $a$ vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.
$I$ - kinetic energy
$II$- gravitational potential energy
$III$ - momentum
Which of these quantities will change as this sphere moves around the circle?
A particle $(\mathrm{m}=1\; \mathrm{kg})$ slides down a frictionless track $(AOC)$ starting from rest at a point $A$ (height $2\; \mathrm{m}$ ). After reaching $\mathrm{C}$, the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height $1 \;\mathrm{m}$ ). the kinetic energy of the particle (in $\mathrm{J}$ ) is : (Figure drawn is schematic and not to scale; take $\left.g=10 \;\mathrm{ms}^{-2}\right)$
A particle $(\mathrm{m}=1\; \mathrm{kg})$ slides down a frictionless track $(AOC)$ starting from rest at a point $A$ (height $2\; \mathrm{m}$ ). After reaching $\mathrm{C}$, the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height $1 \;\mathrm{m}$ ). the kinetic energy of the particle (in $\mathrm{J}$ ) is : (Figure drawn is schematic and not to scale; take $\left.g=10 \;\mathrm{ms}^{-2}\right)$
- [JEE MAIN 2020]
A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is
A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is
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 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 .................. $\mathrm{km}$
- [JEE MAIN 2013]
A bullet of mass $0.02\, kg$ travelling horizontally with velocity $250\, ms^{-1}$ strikes a block of wood of mass $0.23\, kg$ which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of $40\,m$. The coefficient of sliding friction of the rough surface is $(g = 9.8\, ms^{-2})$
A bullet of mass $0.02\, kg$ travelling horizontally with velocity $250\, ms^{-1}$ strikes a block of wood of mass $0.23\, kg$ which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of $40\,m$. The coefficient of sliding friction of the rough surface is $(g = 9.8\, ms^{-2})$