JEE MAIN - Physics (2021 - 31st August Evening Shift - No. 16)
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-
$${{1 \over 3}}$$
$${{2 \over 3}}$$
$${{1 \over 8}}$$
$${{1 \over 4}}$$
Explanation
_31st_August_Evening_Shift_en_16_2.png)
3MV0 = 2MV2 + MV1
3V0 = 2V2 + V1
120 = 2V2 + 60 $$\Rightarrow$$ V2 = 30 m/s
$${{\Delta K.E.} \over {K.E.}} = {{{1 \over 2}MV_1^2 + {1 \over 2}2MV_2^2 - {1 \over 2}3MV_0^2} \over {{1 \over 2}3MV_0^2}}$$
$$ = {{V_1^2 + 2V_2^2 - 3V_0^2} \over {3V_0^2}}$$
$$ = {{3600 + 1800 - 4800} \over {4800}} = {1 \over 8}$$
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