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Question

A shell of mass 20kgat rest explodes into two fragments whose masses are in the ratio 2:3. The smaller fragment moves with a velocity of 6ms-1. The kinetic energy of the larger fragment is


A

96J

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B

216J

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C

144J

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D

360J

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Solution

The correct option is A

96J


Step 1. Given data

The total mass of the shell is 20kg(kilograms) and the ratio of two masses is 2:3.

Therefore, the masses of the two fragments are

M1=8kgM2=12kg

Where M1is the mass of the smaller fragment

M2 is the mass of the larger fragment

The velocity of the smaller fragments is V1=6ms-1

Step 2. Finding the velocity of the larger fragment

By applying the law of conservation of momentum, we get

M1×V1=M2×V2

Where M1is the mass of the smaller fragment

M2 is the mass of the larger fragment

V1 is the velocity of the smaller fragment

V2 is the velocity of the larger fragment

Now, by applying the values in the above formula. we get,

8×6=12×V2V2=4812V2=4ms(meterpersecond)

Step 3. The kinetic energy of the larger fragment

We know kinetic energy of larger fragment is given by

K.E=12M2V22

Where, K.Eis the kinetic energy

M2 is the mass of the larger fragment

V2 is the velocity of the larger fragment

Now, K.E=12×12×(4)2=6×16=96J

Hence, the correct option is (A).


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