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Question

$Time\, period\, of\, spring - block \,system,$

$T=2 \pi \sqrt{\frac{m}{k}}$

For given spring, $T \propto \sqrt{m}$

$\frac{T_{1}}{T_{2}} =\sq

Vedclass · Accepted Answer

$\frac{9}{16}$

Vedclass · Answer

$Time\, period\, of\, spring - block \,system,$

$T=2 \pi \sqrt{\frac{m}{k}}$

For given spring, $T \propto \sqrt{m}$

$\frac{T_{1}}{T_{2}} =\sqrt{\frac{m_{1}}{m_{2}}}$

$	ext { Here, } T_{1} =3 \mathrm{s}, m_{1}=m, T_{2}=5 \mathrm{s}, m_{2}=m+1, m=?$

$ \frac{3}{5}=\sqrt{\frac{m}{m+1}} 	ext { or } \frac{9}{25}=\frac{m}{m+1}$ 

$25 m=9 m+9 \Rightarrow 16 m=9$

$	herefore m=\frac{9}{16} \mathrm{kg}$

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