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:-

• A. 44685
• B. 44900
• C. 44693
• D. 44656

Answer 1

The Correct Option is D

Key Idea : As bodies are dropped from a certain height, their initial velocities are zero ie, $u=0$ For free fall from a height $u = 0$ (initial velocity) From second equation of motion $ h=u t+\frac{1}{2} g t^{2} $ or $ h=0+\frac{1}{2} g t^{2} $ $\therefore \frac{h_{1}}{h_{2}}=\left(\frac{t_{1}}{t_{2}}\right)^{2}$ Given, $h_{1}=16 m , h_{2}=25 \,m$ $\therefore \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{1}}{h_{2}}}$ $=\sqrt{\frac{16}{25}}=\frac{4}{5}$ NOTE : Time taken by the object in falling does not depend on mass of object.