Question

The length of the second's pendulum is decreased by 0.3 cm when it is shifted from place A to place B. If the acceleration due to gravity at place A is 981 cm/s², the acceleration due to gravity at place B is ______ (Take π² = 10)

Options

• 975 cm/s²

• 984 cm/s²

• 978 cm/s²

• 981 cm/s²

Answer 1

The length of the second's pendulum is decreased by 0.3 cm when it is shifted from place A to place B. If the acceleration due to gravity at place A is 981 cm/s², the acceleration due to gravity at place B is 978 cm/s². (Take π² = 10)

Explanation:

For seconds pendulum T = 2s

`T = 2pisqrt(ℓ/g)`

∴ `2 = 2pisqrt(ℓ/g)`

or 1 = `pisqrt(ℓ/g)`

squaring : 1 = `pi^2 ℓ/g`

∴ ℓ = `9/pi^2 = 981/10 = 98.1` cm

At place B, ℓ' = 98.1 - 0.3 = 97.8 cm

Again, 2 = `2pisqrt((ℓ^')/(g^')`

∴ 1 = `pi^2 (ℓ^')/(g^')`

∴ g' = π² ℓ' = 10 × 97.8 = 978 cm/s²