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 $h$. The maximum height h attained by the particle is
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 $h$. The maximum height h attained by the particle is
- A
$\left( {\frac{m}{{m + M}}} \right)\frac{{v_0^2}}{{2g}}$
- B
$\left( {\frac{m}{M}} \right)\frac{{v_0^2}}{{2g}}$
- C
$\left( {\frac{M}{{m + M}}} \right)\frac{{v_0^2}}{{2g}}$
- D
none of these
Similar Questions
A light spring of length $20\, cm$ and force constant $2\, kg/cm$ is placed vertically on a table. A small block of mass $1\, kg$. falls on it. The length $h$ from the surface of the table at which the ball will have the maximum velocity is ............... $\mathrm{cm}$
A light spring of length $20\, cm$ and force constant $2\, kg/cm$ is placed vertically on a table. A small block of mass $1\, kg$. falls on it. The length $h$ from the surface of the table at which the ball will have the maximum velocity is ............... $\mathrm{cm}$
Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.
Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.
A block of mass $M$ has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$, in a co-ordinate system fixed to the table. A point mass $m$ is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is $\mathrm{x}$ and the velocity is $\mathrm{v}$. At that instant, which of the following options is/are correct?
(image)
$[A]$ The $x$ component of displacement of the center of mass of the block $M$ is : $-\frac{m R}{M+m}$.
[$B$] The position of the point mass is : $x=-\sqrt{2} \frac{\mathrm{mR}}{\mathrm{M}+\mathrm{m}}$.
[$C$] The velocity of the point mass $m$ is : $v=\sqrt{\frac{2 g R}{1+\frac{m}{M}}}$.
[$D$] The velocity of the block $M$ is: $V=-\frac{m}{M} \sqrt{2 g R}$.
A block of mass $M$ has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$, in a co-ordinate system fixed to the table. A point mass $m$ is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is $\mathrm{x}$ and the velocity is $\mathrm{v}$. At that instant, which of the following options is/are correct?
(image)
$[A]$ The $x$ component of displacement of the center of mass of the block $M$ is : $-\frac{m R}{M+m}$.
[$B$] The position of the point mass is : $x=-\sqrt{2} \frac{\mathrm{mR}}{\mathrm{M}+\mathrm{m}}$.
[$C$] The velocity of the point mass $m$ is : $v=\sqrt{\frac{2 g R}{1+\frac{m}{M}}}$.
[$D$] The velocity of the block $M$ is: $V=-\frac{m}{M} \sqrt{2 g R}$.
- [IIT 2017]
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 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 ............ $\mathrm{J}$
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.