Question

A uniform metal rod is used as a bar pendulum If
the room temperature rises by 10°C and coefficent
of linear expansion of the metal of the rod is
2x1060 the period of pendulum will increse by
a) 1x10^-7%
3 – 1×10^-3
c) 2×10^-3%
d) -2x10^-7%​

Answer 1

Hello dear,

● Answer- 10^-3

● Explaination-

# Given-

α = 2×10^-6 /°C

ΔT = 10 °C

# Solution-

We know the relation,

Δl/l = αΔT

∆l/l = 2×10^-6 × 10

∆l/l = 2×10^-5

Period of the pendulum is given by-

T = 2π√(l/g)

T = 2π(l/g)^0.5

Therefore, percentage error in period of pendulum will be-

∆T/T×100 = 0.5 × ∆l/l×100

∆T/T×100 = 0.5 × 2×10^-5 × 100

∆T/T×100 = 10^-3

Hope this is helpful...