Work, Energy and Power Difficult Questions and Answers | Page - 1

Work, Energy and Power

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :

1. 100 ms^–1
1. 80 ms^–1
1. 40 ms^–1
1. 120 ms^–1

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Let the initial velocity of the shell be v, then by the conservation of momentum mv = Mv'
where v' = velocity of gun.
∴ v' = m v
M

Now, total K.E. = 1 mv² + 1 Mv'²
2 2

= 1 mv² + 1 M m ² v²
2 2 M

= 1 mv² 1 + m
2 M

= 1 × 0.2 1 + 0.2 v² = (0.1 × 1.05)v²
2 4

But total K.E. = 1.05 kJ = 1.05 × 10³ J
∴ 1.05 × 10³ = 0.1 × 1.05 × v²
v² = 1.05 × 10³ = 10⁴
0.1 × 1.05

∴ v = 10² = 100 ms^–1.

Correct Option: A

Let the initial velocity of the shell be v, then by the conservation of momentum mv = Mv'
where v' = velocity of gun.
∴ v' = m v
M

Now, total K.E. = 1 mv² + 1 Mv'²
2 2

= 1 mv² + 1 M m ² v²
2 2 M

= 1 mv² 1 + m
2 M

= 1 × 0.2 1 + 0.2 v² = (0.1 × 1.05)v²
2 4

But total K.E. = 1.05 kJ = 1.05 × 10³ J
∴ 1.05 × 10³ = 0.1 × 1.05 × v²
v² = 1.05 × 10³ = 10⁴
0.1 × 1.05

∴ v = 10² = 100 ms^–1.