Question 6: Oscillations

Question

A simple pendulum is placed inside a lift, the lift is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio of 1 : 3, then the acceleration of the lift is
[Take acceleration due to gravity, g = 10 m/s
2
]

Accepted Answer

Let a be the acceleration of the lift.
Given, the ratio of time periods of pendulum while the lift is moving upwards and downwards,
T
1
: T
2
= 1 : 3
When lift is moving upwards, then total time period,
$${T_1} = 2\pi \sqrt {{I \over {g + a}}} $$........ (i)
When lift is moving downwards, then total time period,
$${T_2} = 2\pi \sqrt {{I \over {g - a}}} $$ ....... (ii)
Dividing Eq. (i) by Eq. (ii), we get
$${{{T_1}} \over {{T_2}}} = \sqrt {{{g - a} \over {g + a}}}  \Rightarrow {1 \over 3} = \sqrt {{{g - a} \over {g + a}}} $$
or, $${{g - a} \over {g + a}} = {\left( {{1 \over 3}} ight)^2}$$ or, $${{g - a} \over {g + a}} = {1 \over 9}$$
$$ \Rightarrow 9g - 9a = g + a$$
$$ \Rightarrow 9g - g = 9a + a$$
$$ \Rightarrow 10a = 8g$$
$$a = {{8g} \over {10}} = {{8 	imes 10} \over {10}} = 8$$ m/s
2

Answer

4 m/s
2

Answer

6 m/s
2

Answer

8 m/s
2

Answer

10 m/s
2

Oscillations

A simple pendulum is placed inside a lift, the lift is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio of 1 : 3, then the acceleration of the lift is [Take acceleration due to gravity, g = 10 m/s 2 ]

Choose the correct answer: