From a tower of height H, a particle is thrown vertically upwards…

MCQ

From a tower of height $H$, a particle is thrown vertically upwards with a speed $ u$. The time taken by the particle, to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H, u$ and $n$ is:

A
$gH=(n-2)^2u^2$
✓
$2gH=nu^2(n-2)$
C
$gH=(n-2)u^2$
D
$2gH=n^2u^2$

✓

Answer

Correct option: B.

$2gH=nu^2(n-2)$

b
$\begin{array}{l}
Speed\,on\,reaching\,ground\,v = \sqrt {{u^2} + 2gh} \\
Now,\,v = u + at\\
\Rightarrow \,\,\,\,\sqrt {{u^2} + 2gh} = - u + gt\\
Time\,taken\,to\,reach\,highest\,{\rm{point}}\,is\,t = \frac{u}{g},\\
\Rightarrow t = \frac{{u + \sqrt {{u^2} + 2gH} }}{g} = \frac{{nu}}{g}\left( {from\,question} \right)\\
\Rightarrow 2gH = n\left( {n - 2} \right){u^2}
\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 2. motion in straight line→2. motion in straight line — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A uniform chain (mass $M,$ length $L$) is released from rest from a smooth horizontal surface as shown in the figure. Velocity of the chain at the instant it completely comes out of the table will be

→

A person sitting in a chair in a satellite feels weightless because:

→

Match the columns

Column $-I$ $R/H_{max}$	Column $-II$ Angle of projection $\theta $
$A.$ $1$	$1.$ ${60^o}$
$B.$ $4$	$2.$ ${30^o}$
$C.$ $4\sqrt 3$	$3.$ ${45^o}$
$D.$ $\frac {4}{\sqrt 3}$	$4.$ $tan^{-1}\,4\,=\,{76^o}$