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:

Correct answer: A. 4 / 5 We know that time taken by a body from height h to reach the ground is. aligned t & = (2 h)/(g) t_ A t_ B & = 2 h_ A g 2 h_ B g = h_ A h_ B & = (16)/(25) =(4)/(5) . aligned

NEET 2006

Exam: NEET
Year: 2006
Subject: Physics
Chapter: Motion in One Dimension

NEET 2006 · Physics · Motion in One Dimension

Two bodies A (of mass 1 ~kg ) and B (of mass 3 ~kg ) are dropped...

Two bodies

\mathrm{A}

(of mass

1 \mathrm{~kg}

)

and \mathrm{B}

(of mass

3 \mathrm{~kg}

) are dropped from heights of

16 \mathrm{~m}

and

25 \mathrm{~m}

, respectively. The ratio of the time taken by them to reach the ground is:

Options

A $4 / 5$
B $5 / 4$
C $12 / 5$
D $5 / 12$

Correct answer

A. $4 / 5$

Step-by-step solution

We know that time taken by a body from height

h

to reach the ground is.

\begin{aligned}t & =\sqrt{\frac{2 h}{g}}\\ \therefore \quad \frac{t_{\mathrm{A}}}{t_{\mathrm{B}}}& =\frac{\frac{2 h_{\mathrm{A}}}{g}}{\frac{2 h_{\mathrm{B}}}{g}}=\sqrt{\frac{h_{\mathrm{A}}}{h_{\mathrm{B}}}}\\ & =\sqrt{\frac{16}{25}}=\frac{4}{5} . \end{aligned}

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