If the maximum percentage error in the measurement of distance (h) and time ( t ) are ' e₁ ' and ' e₂ ' respectively, the percentage error in the measurement of acceleration of gravity ( g ) is [use h = 1 2 gt ^2 ]

Step-by-step solution

The acceleration due to gravity is derived from h = 1 2 gt^2 , giving g = 2ht⁻² . For a quantity of form X = kA^aB^b , the maximum fractional error is X X = |a| A A + |b| B B . Applying this to g : g g = h h + 2 t t . Multiplying by 100 gives the percentage error: ( g g ) 100 = ( h h ) 100 + 2 ( t t ) 100 . With percentage errors e₁ for height and e₂ for time: Percentage error in g = e₁ + 2e₂ . Final Answer: D