Q129 / 160 · TS EAMCET 2023 (12 May Shift 2) · Physics
A clock is designed based on the oscillations of a springblock system suspended vertically in the absense of air-resistance. Assume it shows the correct time when a spring of stiffness ' $\mathrm{k}$ ' and block of mass ' $\mathrm{m}$ ' are used. If the block is replaced by another block of mass $4 \mathrm{~m}$, choose the correct option.
- Correct answerAThe clock runs slow by $0.5 \mathrm{~s}$ for every one second
- BThe clock runs fast by $0.5 \mathrm{~s}$ for every one second
- CThe clock runs fast by $1 \mathrm{~s}$ for every one second
- DThe clock runs slow by 1 s for every one second
Solution
Time period of a spring block system is given by
$$
\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}
$$
If block of mass " $\mathrm{m}$ " is replaced by block of mass " $4 \mathrm{~m}$ ", then time period is given by
$$
\begin{aligned}
& \mathrm{T}^{\prime}=2 \pi \sqrt{\frac{4 \mathrm{~m}}{\mathrm{k}}} \\
& =2 \pi(2) \sqrt{\frac{\mathrm{n}}{\mathrm{k}}}
\end{aligned}
$$
Using Equation (i),
$$
\mathrm{T}^{\prime}=2 \mathrm{~T}
$$
Thus the time taken is twice.
Hence, the correct answer is option: 'A'.