SATHEE: Work Energy And Power Question 304

Work Energy And Power Question 304

Question: A body of mass M splits into two parts $α$ and $(1 - α)$ M by an internal explosion which generates kinetic energy T. After explosion if the two parts move in the same direction as before, their relative speed will be -

Options:

A) $\sqrt{\frac{T}{(1 - α) M}}$

B) $\sqrt{\frac{2 T}{α (1 - α) M}}$

C) $\sqrt{\frac{T}{2 (1 - α) M}}$

D) $\sqrt{\frac{2 T}{(1 - a) M}}$

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Let the speed of the body before explosion be u.

After explosion, if the two parts move with velocities $u_{1}$

and $u_{2}$ in the same direction, then according to conservation of momentum,

Or $M u_{1} + (1 - α) M u^{2} = M u$

The kinetic energy T liberated during explosion is given

by $T = \frac{1}{2} α M u_{1}^{2} + \frac{1}{2} (1 - α) M u_{2}^{2} - \frac{1}{2} M u^{2}$

$= \frac{1}{2} α M u_{1}^{2} + \frac{1}{2} (1 - α) M u_{2}^{2} - \frac{1}{2 M}$

${[α M u_{1} + (1 - α) M u_{2}]}^{2}$

$= \frac{1}{2} M α (1 - α) [u_{1}^{2} + u_{2}^{2} - 2 u_{1} u_{2}]$

${(u_{1} - u_{2})}^{2} = \frac{2 T}{α (1 - α) M}$

$\Rightarrow (u_{1} - u_{2}) = \sqrt{\frac{2 T}{α (1 - α) M}}$

Work Energy And Power Question 304

Question: A body of mass M splits into two parts $α$ and $(1 - α)$ M by an internal explosion which generates kinetic energy T. After explosion if the two parts move in the same direction as before, their relative speed will be -

Options:

Answer:

Solution:

Engineering Preparation

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NCERT Books & Solutions

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Other Resources

Syllabus

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Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Work Energy And Power Question 304

Question: A body of mass M splits into two parts α and (1−α) M by an internal explosion which generates kinetic energy T. After explosion if the two parts move in the same direction as before, their relative speed will be -

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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Question: A body of mass M splits into two parts $α$ and $(1 - α)$ M by an internal explosion which generates kinetic energy T. After explosion if the two parts move in the same direction as before, their relative speed will be -