A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T . If the mass is increased by m , the time period becomes 5 T / 3 . Then the ratio of m / M is

Question

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T . If the mass is increased by m , the time period becomes 5 T / 3 . Then the ratio of m / M is, 3 / 5, 25 / 9, 16 / 9, 5 / 3

MARKS App · Accepted Answer

Initially, T = 2 π M / k Finally, 5 T 3 = 2 π M + m k ∴ 5 3 × 2 π M k = 2 π M + m k or 25 9 M k = M + m k or 9 m + 9 M = 25M or m M = 16 9 .

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