Two particles having position vectors $\overrightarrow {{r_1}} = (3\hat i + 5\hat j)$ metres and $\overrightarrow {{r_2}} = ( - 5\hat i - 3\hat j)$ metres are moving with velocities ${\overrightarrow v _1} = (4\hat i + 3\hat j)\,m/s$ and ${\overrightarrow v _2} = (\alpha \,\hat i + 7\hat j)$ $m/s.$ If they collide after $2$ seconds, the value of $'\alpha '$ is
Two particles having position vectors $\overrightarrow {{r_1}} = (3\hat i + 5\hat j)$ metres and $\overrightarrow {{r_2}} = ( - 5\hat i - 3\hat j)$ metres are moving with velocities ${\overrightarrow v _1} = (4\hat i + 3\hat j)\,m/s$ and ${\overrightarrow v _2} = (\alpha \,\hat i + 7\hat j)$ $m/s.$ If they collide after $2$ seconds, the value of $'\alpha '$ is
- A
$2$
- B
$4$
- C
$6$
- D
$8$
Similar Questions
Two particles of masses $m_1$ and $m_2$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t$ = $0$ . they collide at time $t_0$ . Their velocities become ${\vec v_1'}$ and ${\vec v_2'}$ at time $2t_0$ while still moving in air. The value of $\left| {\left( {{m_1}{{\vec v}_1}' + {m_2}{{\vec v}_2}'} \right) - \left( {{m_1}{{\vec v}_1} + {m_2}{{\vec v}_2}} \right)} \right|$ is
Two particles of masses $m_1$ and $m_2$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t$ = $0$ . they collide at time $t_0$ . Their velocities become ${\vec v_1'}$ and ${\vec v_2'}$ at time $2t_0$ while still moving in air. The value of $\left| {\left( {{m_1}{{\vec v}_1}' + {m_2}{{\vec v}_2}'} \right) - \left( {{m_1}{{\vec v}_1} + {m_2}{{\vec v}_2}} \right)} \right|$ is
In $a$ one dimensional collision between two identical particles $A$ and $B, B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A.$
In $a$ one dimensional collision between two identical particles $A$ and $B, B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A.$
This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement $- 1$: A point particle of mass m moving with speed $u$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f$ $\left( {\frac{1}{2}m{v^2}} \right)$ then $ f = \left( {\frac{m}{{M + m}}} \right)$
Statement $-2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement $- 1$: A point particle of mass m moving with speed $u$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f$ $\left( {\frac{1}{2}m{v^2}} \right)$ then $ f = \left( {\frac{m}{{M + m}}} \right)$
Statement $-2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
- [JEE MAIN 2013]
Two particles of masses ${m_1}$ and ${m_2}$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t = 0$. They collide at time ${t_0}$. Their velocities become ${\vec v_1}'$ and ${\vec v_2}'$ at time $2{t_0}$ while still moving in air. The value of $|({m_1}\overrightarrow {{v_1}} '\, + {m_2}\overrightarrow {{v_2}} ') - ({m_1}\overrightarrow {{v_1}} \, + {m_2}\overrightarrow {{v_2}} )$| is
Two particles of masses ${m_1}$ and ${m_2}$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t = 0$. They collide at time ${t_0}$. Their velocities become ${\vec v_1}'$ and ${\vec v_2}'$ at time $2{t_0}$ while still moving in air. The value of $|({m_1}\overrightarrow {{v_1}} '\, + {m_2}\overrightarrow {{v_2}} ') - ({m_1}\overrightarrow {{v_1}} \, + {m_2}\overrightarrow {{v_2}} )$| is
- [IIT 2001]
A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?
A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?