Question 106: Work, Energy and Power & Circular Motion

Question

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 :-

Accepted Answer

3MV
0
= 2MV
2
+ MV
1
3V
0
= 2V
2
+ V
1
120 = 2V
2
+ 60 $$\Rightarrow$$ V
2
= 30 m/s
$${{\Delta K.E.} \over {K.E.}} = {{{1 \over 2}MV_1^2 + {1 \over 2}2MV_2^2 - {1 \over 2}3MV_0^2} \over {{1 \over 2}3MV_0^2}}$$
$$ = {{V_1^2 + 2V_2^2 - 3V_0^2} \over {3V_0^2}}$$
$$ = {{3600 + 1800 - 4800} \over {4800}} = {1 \over 8}$$

Answer

$${{1 \over 3}}$$

Answer

$${{2 \over 3}}$$

Answer

$${{1 \over 8}}$$

Answer

$${{1 \over 4}}$$

Work, Energy and Power & Circular Motion

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 :-

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