SATHEE: Work Energy And Power Question 318

Work Energy And Power Question 318

Question: The ratio of masses of two balls is 2 : 1 and before collision the ratio of their velocities is 1 : 2 in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If e = (5/6), the ratio of speed of each ball before and after collision would be

Options:

A) (5/6) times

B) Equal

C) Not related

D) Double for the first ball and half for the second ball

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Let masses of the two ball are 2 m and m and their speeds are u and 2u, respectively.

By conservation of momentum,

$m_{1} {\vec{u}}_{1} + m_{2} {\vec{u}}_{2} = m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}$

$\Rightarrow 2 m u - 2 m u = m v_{2} - 2 m v_{1} \Rightarrow v_{2} = 2 v_{1}$

Coefficient of restitution

$= - \frac{(v_{2} - v_{1})}{(u_{2} - u_{1})} = - \frac{(2 v_{1} + v_{1})}{(- 2 u - u)} = \frac{- 3 v_{1}}{- 3 u} = \frac{- 3 v_{1}}{- 3 u} = \frac{v_{1}}{u} = \frac{5}{6}$ [as given]

$\Rightarrow \frac{v_{1}}{u_{1}} = \frac{5}{6} =$ ratio of the speed of first ball before and after collision.

Similarly, we can calculate the ratio of second ball before and after collision,

$\frac{v_{2}}{u_{2}} = \frac{2 v_{1}}{2 u} = \frac{v_{1}}{u} = \frac{5}{6}$

Work Energy And Power Question 318

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Work Energy And Power Question 318

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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