A shell in free space initially at rest explodes into two pieces, $A$ and $B$ , which then move in opposite directions. Piece $A$ has less mass than piece $B$ . Ignore all external forces. Identify correct statement
A shell in free space initially at rest explodes into two pieces, $A$ and $B$ , which then move in opposite directions. Piece $A$ has less mass than piece $B$ . Ignore all external forces. Identify correct statement
- A
Both have the same momentum after the explosion
- B
Piece $B$ has greater magnitude of momentum after the explosion
- C
Piece $A$ has greater kinetic energy after the explosion
- D
Both have the same kinetic energy after the explosion
Similar Questions
A bullet of mass m moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the block will be
A bullet of mass m moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the block will be
The potential energy function for a particle executing linear simple harmonic motion is given by $V(x)=$ $k x^{2} / 2,$ where $k$ is the force constant of the oscillator. For $k=0.5\; N m ^{-1}$ the graph of $V(x)$ versus $x$ is shown in Figure. Show that a particle of total energy $1 \;J$ moving under this potential must 'turn back" when it reaches $x=\pm 2 m$
The potential energy function for a particle executing linear simple harmonic motion is given by $V(x)=$ $k x^{2} / 2,$ where $k$ is the force constant of the oscillator. For $k=0.5\; N m ^{-1}$ the graph of $V(x)$ versus $x$ is shown in Figure. Show that a particle of total energy $1 \;J$ moving under this potential must 'turn back" when it reaches $x=\pm 2 m$
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 ............... $\mathrm{cm}$
A projectile moving vertically upwards with a velocity of $200\, ms^{-1}$ breaks into two equal parts at a height of $490\, m$. One part starts moving vertically upwards with a velocity of $400\, ms^{-1}$. How much time it will take, after the break up with the other part to hit the ground? .............. $\mathrm{s}$
A projectile moving vertically upwards with a velocity of $200\, ms^{-1}$ breaks into two equal parts at a height of $490\, m$. One part starts moving vertically upwards with a velocity of $400\, ms^{-1}$. How much time it will take, after the break up with the other part to hit the ground? .............. $\mathrm{s}$
- [AIEEE 2012]
Two particles, $1$ and $2$ , each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude a and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t)=\left(x_0+d\right)+a \sin \omega t$ and $x_2(t)=\left(x_0-d\right)-$ $a$ sin $\omega t$, respectively, where $d>2 a$. Particle $3$ of mass $m$ moves towards this system with speed $u_0=a \omega / 2$, and undergoes instantaneous elastic collision with particle 2 , at time $t_0$. Finally, particles $1$ and $2$ acquire a center of mass speed $v_{ cm }$ and oscillate with amplitude $b$ and the same angular frequency. . . . .
($1$) If the collision occurs at time $t_0=0$, the value of $v_{ cm } /(a \omega)$ will be
($2$) If the collision occurs at time $t_0=\pi /(2 \omega)$, then the value of $4 b^2 / a^2$ will be
Give the answer or quetion ($1$) and ($2$)
Two particles, $1$ and $2$ , each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude a and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t)=\left(x_0+d\right)+a \sin \omega t$ and $x_2(t)=\left(x_0-d\right)-$ $a$ sin $\omega t$, respectively, where $d>2 a$. Particle $3$ of mass $m$ moves towards this system with speed $u_0=a \omega / 2$, and undergoes instantaneous elastic collision with particle 2 , at time $t_0$. Finally, particles $1$ and $2$ acquire a center of mass speed $v_{ cm }$ and oscillate with amplitude $b$ and the same angular frequency. . . . .
($1$) If the collision occurs at time $t_0=0$, the value of $v_{ cm } /(a \omega)$ will be
($2$) If the collision occurs at time $t_0=\pi /(2 \omega)$, then the value of $4 b^2 / a^2$ will be
Give the answer or quetion ($1$) and ($2$)
- [IIT 2024]