Question

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Answer 1

Question :

The mass of the bob of a simple pendulum of length L is m. If the bob is left from its horizontal position then the speed of the bob and tension in the thread at the lowest position of the bob will be respectively :-

Answer :

Velocity at lower point can be calculated by using concept of mechanical energy conservation$.$

• E₁ = E₂

E₁ denotes mechanical energy at point 1

E₂ denotes mechanical energy at point 2

We know that, E = K + U

➝ K₁ + U₁ = K₂ + U₂

➝ 0 + mgL = 1/2 mv² + 0

➝ v²/2 = gL

➝ v² = 2gL

➝ v = √2gL ..... (I)

Applying force equation at point 2,

• mv²/L = T - mg

T denotes tension tension force

mv²/L denotes centripetal force

mg denotes weight force

➝ T = mv²/L + mg

From equation (I),

➝ T = m(√2gL)²/L + mg

➝ T = 2mg + mg

➝ T = 3mg ..... (II)

∴ (A) is the correct answer!