NTSE Stage 2 SAT 2017 Question Paper

Question : 37 of 100

Marks: +1, -0

An object of mass ‘m’ moving along a straight line with a velocity ‘u’ collides with a heavier mass ‘M' and gets embedded into it. If the compound system of mass (m + M) keeps moving in the same direction then which of the given options is true ?

The kinetic energies before and after collision are same.
The kinetic energy after collision is $1/2(\M+\m)\u^2$
There will be a loss of kinetic energy equal to $1/2{\m^2\u^2}/{(\M+\m)}$
There will be a loss of kinetic energy equal to $1/2\Mm/{(\M+\m)}\u^2$

Validate

Solution:

By law of conservation of momentum

\mu=(\M+\m)\V

⇒

\v=\mu/{\M+\m}

Change in

\KE=\KE_\f+\KE_\i

\KE_\i=1/2\mu^2,

\KE_\f=1/2(\M+\m)\v^2

=1/2{\m^2\u^2}/{\M+\m}

∴ Change in

\KE=1/2\Mm/{(\M+\m)}\u^2

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