Work Energy and Power - Result Question 57

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

(a) 100ms1

(b) 80ms1

(c) 40ms1

(d) 120ms1

[2008]

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Answer:

Correct Answer: 60. (a)

Solution:

  1. (a) Let the initial velocity of the shell be v, then by the conservation of momentum mv=Mv where v= velocity of gun.

v=(mM)v

Now, total K.E. =12mv2+12Mv2

=12mv2+12M(mM)2v2

=12mv2[1+mM]

=(12×0.2)(1+0.24)v2=(0.1×1.05)v2

But total K.E. =1.05kJ=1.05×103J

1.05×103=0.1×1.05×v2

v2=1.05×1030.1×1.05=104

v=102=100ms1.



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