CBSE Class 11-science Answered

A ball suspended by a thread swings in a vertical plane so that its acceleration values in the extreme and the lowest position are equal. Find the thread deflection angle in the extreme position.

Asked by Vivek.d8765 | 25 Jun, 2018, 11:09: AM

Expert Answer

At extreme position A, as shown in figure, speed of the ball is zero. Hence no centripetal force.

Acceleration is only due to gravity and the acceleration is resolved in the direction of motion as g sinθ as shown in figure.

In the lowest position O, acceleration is calculated as follows.

When the ball reaches the point O with maximum speed v,

potenial difference due to height h is fully converted to kinetic energy.

hence we have

begin mathsize 12px style 1 half m space v squared space equals space m cross times g cross times h space equals space m cross times g cross times open parentheses R minus R cos theta close parentheses end style

.................(1)

eqn.(1) is simplified to

begin mathsize 12px style v squared over R space equals space 2 cross times g cross times open parentheses 1 minus cos theta close parentheses end style

..................(2)

LHS of eqn.(2) is acceleration at point O.

hence we have g sinθ = 2×g×(1 - cosθ) or

begin mathsize 12px style fraction numerator open parentheses 1 space minus space cos space theta close parentheses over denominator sin space theta end fraction space equals space fraction numerator 2 space sin squared begin display style theta over 2 end style over denominator 2 space sin begin display style theta over 2 end style cos space begin display style theta over 2 end style end fraction space equals space tan theta over 2 space equals 1 half end style

........(3)

solving eqn.(3) for θ, we get θ = 53°

Answered by Thiyagarajan K | 25 Jun, 2018, 03:33: PM

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CBSE Class 11-science Answered

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