Six pendulums of mass mand length Las shown are released from rest at the same angle theta from vertical. Rank the pendulums according to the numberof complete cycles of motion each pendulum goes through perminute.
A. L= 1m
m=2kg
B. L= 4m
m=1 kg
C. L= 2 m
m= 2 kg
D. L= 1 m
m= 4 kg
E. L= 2 m
m = 4 kg
F. L= 4m
m = 4kg

Explanation:

Time period of pendulum is given by the following formula

T = 2π√(L / g) T is time period , L is length of pendulum , g is acceleration due to gravity. Time period does not depend upon mass of the bob.

Time period of first pendulum T₁ =  2π√( 1/ g)

Time period of second pendulum T₂ =  2π√( 4/ g)

Time period of third pendulum T₃ =  2π√( 2/ g)

Time period of fourth pendulum T₄ =  2π√( 1/ g)

Time period of fifth pendulum T₅ =  2π√( 2/ g)

Time period of sixth pendulum T₆ =  2π√( 4/ g)

T₂=T₆> T₃ =T₅>T₁=T₄

frequency  or number of cycles per minute will be inversely related to time period. so

N₂ = N₆>N₃=N₅>N₁=N₄

N represents no of oscillation per minute .