Tag: collisions

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

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  $10 m / s ^ { 2 }.$

  1. $4 s$
  2. $2 s$
  3. $0.8 s$
  4. $1.2 s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time taken to reach the highest point after the rebound at speed v = 10 m/s is t_up = v/g = 10/10 = 1 s. However, the ceiling is at a height of 3.2 m. Using kinematic equation y = v*t - (1/2)*g*t^2, at y = 3.2m we get 3.2 = 10*t - 5*t^2, which solves to t = 0.4 s (the ball hits the ceiling before reaching its natural peak of 5m). The collision with the ceiling reverses the velocity, so the round trip time until it returns to the floor is 0.8 s.

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

 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 :

  1. 1 kg only

  2. 1 kg , 9kg

  3. 1 kg, 6kg

  4. 6kg only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial kinetic energy of the 3 kg ball is (1/2)3(4)^2 = 24 J. After an elastic collision, its kinetic energy is 6 J. Using the conservation of kinetic energy and momentum for an elastic collision in 1D, the final speed of the 3 kg mass can be found, leading to possible mass values of m = 1 kg or m = 9 kg.

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

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 

  1. $\dfrac{400}{3} J$
  2. $\dfrac{500}{3} J$
  3. $100 J$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In any isolated system undergoing an elastic collision, total kinetic energy is conserved. Thus, the decrease in kinetic energy of one body must equal the increase in kinetic energy of the other body. Since one body loses 100 J, the other body gains exactly 100 J, regardless of their mass ratio.

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

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

  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. $- 0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two identical masses collide elastically in one dimension, they simply exchange their velocities. Since A starts at 0.5 m/s and B at -0.3 m/s, after the collision, A will have -0.3 m/s and B will have 0.5 m/s.

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

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-

  1. $ \overrightarrow { u } $
  2. $ - \overrightarrow { u } $
  3. $ 2 \overrightarrow { u } $
  4. $ -2 \overrightarrow { u } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a head-on elastic collision where a very massive body (m1) hits a stationary light body (m2), the velocity of the light body after the collision is twice the velocity of the incident massive body.

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

Which of the following does no undergo elastic collision?

  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.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

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 

  1. $1:1$
  2. $1:2$
  3. $2:1$
  4. $1:4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A ball falling freely from height h takes time t = sqrt(2h/g) to reach the floor. For a perfectly elastic collision, it rebounds with the same speed and takes the same time t to return to the original height. The total time elapsed before it hits the floor again is t' = 2t, making the ratio t' to t equal to 2:1.

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

A sphere P of mass m and  velocity $\underset{V _{1}}{\rightarrow}$  undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest.  The  angle $\Theta $  between the velocites of the spheres after the collision shall be

  1. 0
  2. $45^{\circ}$
  3. $90^{\circ}$
  4. $180^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a perfectly elastic collision between two identical masses where one is initially at rest, the two bodies will move at an angle of 90 degrees to each other after the collision, provided the collision is oblique.