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Question

# A spring is made to oscillate after suspending a mass m from one of its ends. The time period obtained is 2 seconds. On increasing the mass by 2 kg, the period of oscillation is increased by 1 second. The initial mass m will be :

A
2 kg
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B
1 kg
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C
0.5 kg
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D
1.6 kg
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Solution

## The correct option is D 1.6 kgWe know that , T∝2π√mk where T is the time period , m is the initial mass and k is the spring constant . Thus we can say , T∝√m 2s∝√m -------- (i) 2s+1s∝√m+2 Or 3s∝√m+2 -----------(ii) Dividing (ii) by (i) 3s2s=K√m+2√m \\ where K is a constant Or,(3)2(2)2=m+2m // squaring both sides Or, 9m=4m+8 Or, 5m=8 Or, m=1.6kg

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