A simple pendulum of length 100cm is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination 60∘. Find the time period of the pendulum.
Take g=10m/s2.
A
2s
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B
2.8s
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C
5s
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D
2.14s
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Solution
The correct option is B2.8s Length of simple pendulum, l=100cm
Angle of inclination (θ)=60∘
Acceleration of cart along the inclined plane is, a=mgsinθm=gsinθ
Weight(mg) can be resolved into two components mgsinθ along the plane and mgcosθ perpendicular to the plane.
Effective weight of pendulum bob, m→g′=m→g+−→FP...(1)
where FP=ma=mgsinθ acts on bob, in a direction opposite to its acceleration.(Pseudo force) After vectorial addition from Eq.(1), ⇒mg′=mgcosθ ∴g′=gcosθ
Hence geff=gcosθ
Time period of pendulum in the cart is given as, T=2π√lgeff ⇒T=2π√lgcosθ∴T=2×3.14×√15=2.8s