Question

The acceleration of free fall of a planet is determined by timing the fall of a steel wall photo electrically. The ball passes B and C at times T1 and t2 after released from A acceleration of free fall is given by

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Answer 1

Given info : The acceleration of free fall of a planet is determined by timing the fall of a steel wall photo electrically. The ball passes B and C at times t₁ and t₂ after released from A.

To find : The acceleration of free fall is given by,

solution : The ball falls freely from A and reaches point B at time t = t₁

initial velocity of ball, u = 0

let acceleration of free fall is a.

using formula, s = ut + 1/2 at²

⇒s = 0 + 1/2 at₁² .......(1)

in 2nd case , The ball falls from A and reaches point C at time t = t₂

here S' = s + h

using formula, s = ut + 1/2 at²

⇒s + h = 0 + 1/2 at₂² .........(2)

from equations (1) and (2) we get,

s + h - s = 1/2 at₂² - 1/2 at₁²

⇒h = 1/2 a(t₂² - t₁²)

⇒a = 2h/(t₂² - t₁²)

Therefore the acceleration of free fall is given by, a = 2h/(t₂² - t₁²).

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