Question 172: Oscillations

Question

The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillation of the bob is $${t_0}$$ in air. Neglecting frictional force of water and given that the density of the bob is $$\left( {4/3} ight) 	imes 1000\,\,kg/{m^3}.$$ What relationship between $$t$$ and $${t_0}$$  is true

Accepted Answer

$$t = 2\pi \sqrt {{\ell  \over {{g_{eff}}}}} ;\,{t_o}\,\, = 2\pi \sqrt {{\ell  \over g}} $$
$$m{g_{eff}} = mg - B = my - V 	imes 100 	imes g$$
$$	herefore$$ $${g_{eff}} = g - {{100} \over {\left( {m/v} ight)}}g$$
$$ = g - {{1000} \over {{4 \over 3} 	imes 1000}}g = {g \over 4}$$
$$	herefore$$ $$t = 2\pi \sqrt {{\ell  \over {g/4}}} \,\,\,\,\,\,\,\,\,\,\,t = 2{t_0}$$

Answer

$$t = 2{t_0}$$

Answer

$$t = {t_0}/2$$

Answer

$$t = {t_0}$$

Answer

$$t = 4{t_0}$$

Oscillations

Choose the correct answer: