Oscillations
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Question : 8
Total: 25
A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?
Solution:
Here, m = 50 kg,
Maximum extension, y = 20 – 0 = 20 cm = 0.2 m
Maximum force, F = mg = 50 × 9.8 = 490 N
∴ Spring constant,
k =
=
=
= 2450 Nm − 1
When a body of mass M is suspended from the spring balance, it oscillates with a period of 0.6 s.
∵ Time period,T = 2 π √
T 2 = 4 π 2
∴ M =
=
M = 22.36 kg
∴ Weight of the body,
W = Mg = 22.36 × 9.8 = 219.1 N = 22.36 kgf
Maximum extension, y = 20 – 0 = 20 cm = 0.2 m
Maximum force, F = mg = 50 × 9.8 = 490 N
∴ Spring constant,
When a body of mass M is suspended from the spring balance, it oscillates with a period of 0.6 s.
∵ Time period,
M = 22.36 kg
∴ Weight of the body,
W = Mg = 22.36 × 9.8 = 219.1 N = 22.36 kgf
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