First slide

Applications of SHM

Question

Restoring force on the bob of a simple pendulum of mass 100 g when its amplitude is 1° is (here acceleration due to gravity =10m $s^{- 2}$ )

Moderate

A

0.017 N
B

1.7 N
C

0.17 N
D

0.034 N

Solution

$R e s t o r i n g f o r c e o n s i m p l e p e n d u l u m = F_{R} = m g \sin θ h e r e θ i s v e r y s m a l l, h e n c e \sin θ ≃ θ \Rightarrow F_{R} = m g θ = 100 \times 10^{-3} \times 10 \times 1^{\circ}, h e r e 1^{\circ} = \frac{π}{180}, s u b s t i t u t e = \frac{1000}{1000} \times \frac{π}{180} \Rightarrow F_{R} = \frac{3.14}{180} = 0.017 N$

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