Potential energy vs. position graph of a particle in particular system is given and here P.E. is U=a x2. There is a non-conservative force also acting on a particle in such a manner that mechanical energy loss due to its work is equal to four times of its distance travelled. Initially particle is at x=10, has kinetic energy 36 J and moving towards origin. The kinetic energy of particle (in m ) when it reaches origin second time is .

Question

Potential energy vs. position graph of a particle in particular system is given and here P.E. is U=a x2. There is a non-conservative force also acting on a particle in such a manner that mechanical energy loss due to its work is equal to four times of its distance travelled. Initially particle is at x=10, has kinetic energy 36 J and moving towards origin. The kinetic energy of particle (in m ) when it reaches origin second time is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Applying work energy theorem 100+36=x02+4(10+x0) ⇒ x0=8 Again apply work energy theorem, 64-32=Δ KE and 32 J = KE

Applying work energy theorem 100+36=x02​+4(10+x0​) ⇒x0​=8 Again apply work energy theorem, 64−32=ΔKE and 32J=KE

Applying work energy theorem
$100 + 36 = x_{0}^{2} + 4 (10 + x_{0})$
$\Rightarrow x_{0} = 8$
Again apply work energy theorem,
$64 - 32 = Δ K E$ and $32 J = K E$