Start Free Mock LoginAlready registered? Login here

Physics - W.E.P. Question with Solution | TestHub

PhysicsW.E.P.Work kinetic energy theoremHard2 minQB

PhysicsHardsingle choice

A body of mass $m$ starts moving from rest along $x -$ axis so that its velocity varies as $v = a \sqrt{s}$ where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first $t$ second after the start of the motion is

Options:

Answer:

Solution:

$v = a \sqrt{s} = \frac{d s}{dt}$

$\Rightarrow \frac{d s}{\sqrt{s}} = a .dt$

$\Rightarrow 2 \sqrt{s} = a t$

$\Rightarrow s = \frac{a^{2} t^{2}}{4}, v = \frac{d s}{dt} = \frac{a^{2} t}{2}$

$\Rightarrow W_{all} = ∆ K = K_{f} - K_{i}$

$\Rightarrow W_{all} = \frac{1}{2} m [v_{2}^{2} - v_{1}^{2}]$

$\Rightarrow v_{1} = 0, v_{2} = \frac{a^{2} t}{2}$

$\Rightarrow W_{all} = \frac{1}{2} m [{(\frac{a^{2} t}{2})}^{2} - 0]$

$\Rightarrow W_{all} = \frac{1}{8} m a^{4} t^{2}$

$\Rightarrow W_{all} = ∆ K$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Work kinetic energy theorem

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...