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  • The acceleration due to gravity is found upto an accurcy of 4% on a planet. The energy supplied to a simple pendulum of known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%,

The acceleration due to gravity is found upto an accurcy of 4% on a planet. The energy supplied to a simple pendulum of known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as______%.
 

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E= mgh= mg\left ( l-l\cos \theta \right )
                      =mgl \left ( 1-\cos \theta \right )
E=mgl \times 2\sin ^{2}\left ( \frac{\theta }{2} \right )
for SHM , \theta \rightarrow 0
\sin \left ( \frac{\theta }{2} \right )= \left ( \frac{\theta }{2} \right )
E= mgl\times 2 \left ( \frac{\theta }{2} \right )^{2}
T= 2\pi \sqrt{\frac{l}{g}} \; \; ;\frac{9T^{2}}{4\pi ^{2}}= l
E= \frac{mg^{2}T^{2}}{4\pi ^{2}}\times 2\left ( \frac{\theta }{2} \right )^{2}
\frac{\Delta E}{E}\times 100= \frac{2\Delta 9}{5}\times 100+\frac{2\Delta T}{T}\times 100
                      = 2\times 4%+2\times 3%
\frac{\Delta E}{E}\times 100= 14%

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vishal kumar

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