0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

A simple pendulum is being used to determine the value of gravitational acceleration $$g$$ at a certain place. The length of the pendulum is $$25.0cm$$ and a stopwatch with $$1s$$ resolution measures the time taken for $$40$$ oscillation to be $$50s$$. The accuracy in $$g$$ is:

A
$$5.40$$%
B
$$4.40$$%
C
$$3.40$$%
D
$$2.40$$%
Solution
Verified by Toppr

Correct option is D. $$4.40$$%
For simple pendulum

$$T = 2\pi \sqrt{\dfrac{l}{g}}$$

so, $$\dfrac{\Delta T}{T} = \dfrac{1}{2} \left(\dfrac{\Delta l}{l} + \dfrac{\Delta g}{g}\right)$$

Givn $$\Delta T = 1 \ sec$$ $$T = 50 sec$$

$$\Delta l = 0.1 cm$$

$$l = 25 cm$$

$$\dfrac{\Delta g}{g} = \dfrac{2\Delta T}{T} + \dfrac{\Delta l}{l}$$

$$\dfrac{\Delta g}{g} = 2\times \dfrac{1}{50} + \dfrac{0.1}{25} = \dfrac{1.1}{25}$$

$$\dfrac{\Delta g}{g} = \dfrac{1.1}{25}$$

$$\% \dfrac{\Delta g}{g} = \dfrac{1.1}{25} \times 100 = 4.4 \%$$

Was this answer helpful?
17
Similar Questions
Q1
A simple pendulum is being used to determine the value of gravitational acceleration $$g$$ at a certain place. The length of the pendulum is $$25.0cm$$ and a stopwatch with $$1s$$ resolution measures the time taken for $$40$$ oscillation to be $$50s$$. The accuracy in $$g$$ is:
View Solution
Q2

A simple pendulum is being used to determine the value of gravitational acceleration at a certain place. The length of the pendulum is 25.0cm measured with accuracy of 0.1cm and a stopwatch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in g


View Solution
Q3
The period of oscillation of a simple pendulum is T=2πLg. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch 0f 1s resolution. The accuracy in the determination of g is:
View Solution
Q4
The period of oscillation of a simple pendulum is T=2πLg. The measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wristwatch of 1s resolution. What is the accuracy in the determination of g?
View Solution
Q5
In an experiment to determine the value of acceleration due to gravity, g, using a simple pendulum, the measured value of length of the pendulum is 31.4 cm known to 1 mm accuracy and the time period for 100 oscillations of pendulum is 112.0 s known to 0.01 s accuracy. The accuracy in determining the value of g is :
View Solution