Question 334: Gravitation

Question

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

Accepted Answer

If $$\mathrm{g}$$ is the acceleration due to gravity on earth's surface and $$\mathrm{g}^{\prime}$$ on the planet, then
$$\begin{aligned}
\mathrm{g} & =\frac{\mathrm{GM}}{\mathrm{r}^2} 	ext { and } \mathrm{g}^{\prime}=\frac{\mathrm{G} 	imes 1.5 \mathrm{M}}{(1.5)^2 \mathrm{r}^2}=\frac{1}{1.5} \frac{\mathrm{GM}}{\mathrm{r}^2} \
	herefore \quad \mathrm{g}^{\prime} & =\frac{\mathrm{g}}{1.5} .
\end{aligned}$$
For second's pendulum $$\mathrm{T}=2 \mathrm{~s}$$
$$\begin{aligned}
& 	herefore \mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}=2 \pi \sqrt{\frac{\ell^{\prime}}{\mathrm{g}^{\prime}}} \
& 	herefore \frac{\ell}{\mathrm{g}}=\frac{\ell^{\prime}}{\mathrm{g}^{\prime}} \quad 	herefore \ell^{\prime}=\ell \cdot \frac{\mathrm{g}^{\prime}}{\mathrm{g}}=1 	imes \frac{1}{1.5}=\frac{2}{3}=0.67 \mathrm{~m}
\end{aligned}$$

Answer

0.67 m

Answer

0.45 m

Answer

0.60 m

Answer

0.76 m

Gravitation

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

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