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 simple harmonic oscillations with a time period T. If the mass is increased by m then the time period becomes$\left( \frac { 5 } { 4 } T \right)$. The ratio of $\frac { m } { M }$ is

• A. 9/16
• B. 25/16
• C. 4/5
• D. 5/4

Answer 1

Answer: (A)

9/16

Answer 2

$T = 2 \pi \sqrt { \frac { m } { k } }$ ⇒ $m \propto T ^ { 2 }$ ⇒ $\frac { m _ { 2 } } { m _ { 1 } } = \frac { T _ { 2 } ^ { 2 } } { T _ { 1 } ^ { 2 } }$

$\Rightarrow \frac { M + m } { M } = \left( \frac { \frac { 5 } { 4 } T } { T } \right) ^ { 2 } \Rightarrow \frac { m } { M } = \frac { 9 } { 16 }$