Question

simple pendulums A and B have equal lengths but their bob weigh 50 gf and
100 gf respectively. What would be the ratio of their time periods? What is the reason for
your answer?​

Answer 1

Answer:

Explanation:

Hi friend!

There's a point to remember while dealing with pendulums:

Time period of pendulums do not depend upon mass. They only depend upon length and magnitude of acceleration due to gravity.

T = 2π$\sqrt{l/g}$

Proof:

We will be using a pinch of rotational mechanics while proving so:

First, draw a pendulum hanging vertically, making an angle of 0 degrees with the vertical.

Now, draw a dotted version of the pendulum, making an angle thetha with the vertical.

The forces acting on the pendulum would only be mg.

The components of mg would be mgsinthetha (acting perpendicular to the length) and mgcosthetha (acting in the direction of length)

We know torque = I x alpha , alpha = w^2 thetha

Torque here would be mgsinthetha x l ( l is the length of the pendulum)

I = m(l^2) ,

mgsinthetha = m(l^2) x w^2 x thetha

mg x thetha = m x l^2 x w^2 x thetha

(when thetha <<< 5 radians, sinthetha = thetha)

Solving it ====> w = $\sqrt{g/l}$

We know T = 2π/w = 2π x $\sqrt{l/g}$

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Answer 2

Answer:

it's your answer hope it helps