Question

A bob of mass 4kg is suspended from a string of length 1m. The bob is pulled to a side till the string makes an angle 60° to the vertical and released Then tension in the string when it reaches the vertical position is Clear Response​

Answer 1

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Answer 2

The tension in the string is 80 N when it reaches the vertical position.

A bob of mass 4 kg is suspended from a string of length 1 m. The bob is pulled to a side till the string makes an angle 60° to the vertical and released.

We have to find the tension in the string when it reaches the vertical position.

We should find the velocity at the vertical position so that we can include centripetal force acting on the string.

From work-energy theorem,

change in kinetic energy = change in potential energy of bob for two positions

⇒ 1/2 mv² - 0 = mgl - mgl cos60°

here v is the velocity of bob at the vertical line.

⇒ v² = 2gl(1 - cos60°)

⇒ v² = 2gl(1 - 1/2) = gl

⇒ v = √(gl)

Now the tension in the string along the vertical position,

⇒ tension - weight = centripetal force

⇒T - mg = mv²/l = m(gl)/l = mg

⇒ T = 2mg = 2 × 4 kg × 10 m/s² = 80 N

Therefore the tension in the string is 80 N.