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 .................(1)
eqn.(1) is simplified to ..................(2)
LHS of eqn.(2) is acceleration at point O.
hence we have g sinθ = 2×g×(1 - cosθ) or ........(3)
solving eqn.(3) for θ, we get θ = 53°
Answered by Thiyagarajan K | 25 Jun, 2018, 03:33: PM
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