Tag: physics

Questions Related to physics

Two particles of masses $ {m} _{1}, {m} _{2} $ movie with initial velocities $ u _{1} \text { and } u _{2} $.On collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be $  v _{1}  $ and $  v _{2}  $ then we must have :

collisions in one dimension collisions work, energy and power mechanics physics

  1. $
    \dfrac{1}{2} m _{1} u _{1}^{2}+\dfrac{1}{2} m _{2} u _{2}^{2}=\dfrac{1}{2} m _{1} v _{1}^{2}+\dfrac{1}{2} m _{2} v _{2}^{2}-\varepsilon
    $

  2. $
    \dfrac{1}{2} m _{1} u _{1}^{2}+\dfrac{1}{2} m _{2} u _{2}^{2}+\varepsilon=\dfrac{1}{2} m _{1} v _{1}^{2}+\dfrac{1}{2} m _{2} v _{2}^{2}
    $

  3. $
    \dfrac{1}{2} m _{1}^{2} u _{1}^{2}+\dfrac{1}{2} m _{2}^{2} u _{2}^{2}-\varepsilon=\dfrac{1}{2} m _{1}^{2} v _{1}^{2}+\dfrac{1}{2} m _{2}^{2} v _{2}^{2}
    $

  4. $
    m _{1}^{2} u _{1}+m _{2}^{2} u _{2}-\varepsilon=m _{1}^{2} v _{1}+m _{2}^{2} v _{2}
    $

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Correct Option: C
Explanation:

$\begin{array}{l} Total\, \, initial\, \, energy\, \, of\, \, two\, \, particles \ =\frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 } \ Total\, \, final\, \, energy\, \, of\, \, two\, particles \ =\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 }+\in  \ U\sin  g\, \, energy\, \, conservation\, \, principle, \ \frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 }=\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 }+\in  \ \therefore \frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 }-\in =\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 } \end{array}$

Hence,
option $(C)$ is correct answer.

A moving sphere of mass m suffer a perfect elastic collision (not head on) with an  equally massive stationary sphere. after collision both fly off at angle $\theta $ value of which is :

collisions in one dimension collisions work, energy and power mechanics physics

  1. 0

  2. $\pi $

  3. indeterminate

  4. $\pi /2$

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Correct Option: D

A rubber ball is bounced on the floor of a room which has its ceiling at a height of  $3.2{ m }$  from the floor. The ball hits the floor with a speed of  $10 m / { s },$  and rebounds vertically up. If all collisions simply reverse the velocity of the ball, without changing its speed, then how long does it take the ball for a round trip, from the moment it bounces from the floor to the moment it returns back to it ? Acceleration due to gravity is  $10 m / s ^ { 2 }.$

collisions in one dimension collisions work, energy and power mechanics physics

  1. $4 s$

  2. $2 s$

  3. $0.8 s$

  4. $1.2 s$

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Correct Option: A

 A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly- elastic collision with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value of m is/are :

collisions in one dimension collisions work, energy and power mechanics physics

  1. 1 kg only

  2. 1 kg , 9kg

  3. 1 kg, 6kg

  4. 6kg only

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Correct Option: A

A proton of mass $m _p$ collides with a heavy particle. After collision proton bunches back with 4/9 of its intial kinetic energy. Collision is perfectly elastic. Find mass of heavy particle.

collisions in one dimension collisions work, energy and power mechanics physics

  1. 5 $m _p$

  2. 6 $m _p$

  3. 3 $m _p$

  4. 1.5 $m _p$

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Correct Option: C

In an elastic collision the K.E of one body decreases by $100 J$. If the masses colliding bodies are in the ratio 3:4 the K.E of the other body increase by 

collisions in one dimension collisions work, energy and power mechanics physics

  1. $\dfrac{400}{3} J$

  2. $\dfrac{500}{3} J$

  3. $100 J$

  4. $0$

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Correct Option: A

Two identical balls  $A$  and  $B$  having velocities of  $0.5\mathrm { m } / \mathrm { s }$  and  $- 0.3 \mathrm { m } / \mathrm { s }$  respectively collide elastically in one dimension. The velocities of  $B$  and  $\mathrm { A }$  after the collision respectively will be

collisions in one dimension collisions work, energy and power mechanics physics

  1. $0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$

  2. $- 0.5 \mathrm { m } / \mathrm { s } \text { and } 0.3 \mathrm { m } / \mathrm { s }$

  3. $0.5 \mathrm { m } / \mathrm { s } \text { and } - 0.3 \mathrm { m } / \mathrm { s }$

  4. $- 0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$

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Correct Option: C

A particle of mass $ m _1 $ hits another particle of mass $ m _2 $ at rest with a velocity $ \overrightarrow { u }  $. The collision is head-on and elastic.If $ m _1 >> m _2 $, then after collision, the velocity of $ m _2 $ will be-

collisions in one dimension collisions work, energy and power mechanics physics

  1. $ \overrightarrow { u } $

  2. $ - \overrightarrow { u } $

  3. $ 2 \overrightarrow { u } $

  4. $ -2 \overrightarrow { u } $

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Correct Option: C

Which of the following does no undergo elastic collision?

collisions in one dimension collisions work, energy and power mechanics physics

  1. When $ m _1 = m _2$ and $m _2 $ is stationary,there is maximum transfer of kinetic energy in head an collision

  2. When $ m _1 = m _2 $ is stationary,there is minimum transfer of momentum in head on collision

  3. When $ m _1 >> m _2 $ is stationary,after head on collision $ m _2 $ moves with twice the velocity of $ m _1 $

  4. When the collision is oblique and $ m _1 = m _2 with m _2 $ stationary,after the collision the particle move in opposite directions.

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Correct Option: A

A perfectly elastic ball falls on a horizontal floor from a height in a time $t$. It will hit the floor again after a time $t'$. The ratio of $t'$ and t is 

collisions in one dimension collisions work, energy and power mechanics physics

  1. $1:1$

  2. $1:2$

  3. $2:1$

  4. $1:4$

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Correct Option: B