A particle is released freely from a height H | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the particle fall from height $H$ and reach a height $h$ from the ground.At this height $h$,the potential energy is $PE = mgh$.The distance fa

Vedclass · Accepted Answer

$\frac{H}{3}, 2 \sqrt{\frac{g H}{3}}$

Vedclass · Answer

(B) Let the particle fall from height $H$ and reach a height $h$ from the ground.At this height $h$,the potential energy is $PE = mgh$.The distance fallen by the particle is $x = H - h$.The kinetic energy at this point is $KE = mgx = mg(H - h)$.According to the problem,$KE = 2(PE)$.Substituting the expressions,we get $mg(H - h) = 2(mgh)$.$H - h = 2h \Rightarrow H = 3h \Rightarrow h = \frac{H}{3}$.Now,to find the speed $v$ at height $h = \frac{H}{3}$,we use the equation of motion $v^2 = u^2 + 2ax$,where $u = 0$ and $x = H - h = H - \frac{H}{3} = \frac{2H}{3}$.$v^2 = 2g(\frac{2H}{3}) = \frac{4gH}{3}$.$v = \sqrt{\frac{4gH}{3}} = 2\sqrt{\frac{gH}{3}}$.Thus,the height is $\frac{H}{3}$ and the speed is $2\sqrt{\frac{gH}{3}}$.

$A$ particle is released freely from a height $H$. At a certain height,its kinetic energy is two times its potential energy. Then,the height and the speed of the particle at that instant are respectively ($g=$ acceleration due to gravity).

Similar Questions

In the non-relativistic regime,if the momentum is increased by $100\%$,the percentage increase in kinetic energy is (in $\%$)

The kinetic energy acquired by a mass $m$ in travelling a certain distance $d$ starting from rest under the action of a constant force is directly proportional to

$A$ particle is dropped from a height $h$. $A$ constant horizontal velocity $u$ is given to the particle. Taking $g$ to be constant everywhere, the kinetic energy $E$ of the particle with respect to time $t$ is correctly shown in:

Two particles of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. The ratio of their momentum is

$A$ body initially at rest is acted upon by a constant force $F$ for time $t$. The kinetic energy at time $t$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module