Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The

Question

Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is:

Accepted Answer

1.  **Identify Kinematic Equation:** For a body falling freely from rest ($u = 0$) under gravity ($a = g$), the distance fallen ($h$) in time ($t$) is given by the equation: 
    $$ h = \frac{1}{2}gt^2 $$
    Solving for time, we get:
    $$ t = \sqrt{rac{2h}{g}} $$
    Note: The time of fall is independent of the mass of the body .
2.  **Calculate Time for Each Body:**
    *   For body A ($h_A = 16$ m): $t_A = \sqrt{rac{2(16)}{g}}$
    *   For body B ($h_B = 25$ m): $t_B = \sqrt{rac{2(25)}{g}}$
3.  **Calculate Ratio:**
    $$ \frac{t_A}{t_B} = \frac{\sqrt{2(16)/g}}{\sqrt{2(25)/g}} = \sqrt{\frac{16}{25}} = \frac{4}{5} $$

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