A mass $M,$ attached to a spring, oscillates with a period of $2 s,$ If the mass is increased by $4 k g,$ the time period increases by one second. Assuming that Hooke's law is obeyed, the initial mass $M$ was:

3.2 k g

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1 k g

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2 k g

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8 k g

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Solution

The correct option is A $3.2 k g$
$2 = 2 π \sqrt{\frac{M}{k}} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (i)$
$3 = 2 π \sqrt{\frac{M + 4}{k}} . . . . . . . . . . . . . . . . . . . . . . . . . . . (i i)$
Solving two equations, we get
$M = 3.2 k g$

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A mass M, attached to a spring, oscillates with a period of 2 s, If the mass is increased by 4 kg, the time period increases by one second. Assuming that Hooke's law is obeyed, the initial mass M was:

The correct option is A 3.2 kg2=2π√Mk..............................(i)3=2π√M+4k...........................(ii)Solving two equations, we getM=3.2 kg

A mass $M,$ attached to a spring, oscillates with a period of $2 s,$ If the mass is increased by $4 k g,$ the time period increases by one second. Assuming that Hooke's law is obeyed, the initial mass $M$ was:

The correct option is A $3.2 k g$
$2 = 2 π \sqrt{\frac{M}{k}} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (i)$
$3 = 2 π \sqrt{\frac{M + 4}{k}} . . . . . . . . . . . . . . . . . . . . . . . . . . . (i i)$
Solving two equations, we get
$M = 3.2 k g$