Question

Match the physical situation on the left with the graph on the right. The graphs depict the variation of total energy $\left(E\right)$, potential energy $\left(U\right)$ and kinetic energy $\left(KE\right)$ with time.

Column I		Column II
i.	A mass attached to an unstretched ideal spring. Released in vertical plane from rest until it reaches its maximum extension	p.
ii.	An object undergoing free fall	q.
iii.	An object being pulled on a level, frictionless sur face by a constant force in the horizontal direction	r.
iv.	A block is coming down on a rough inclined plane with constant velocity	s.

Now match the given columns and select the correct option from the codes given below.
Codes:

• A. i—p, ii—q, iii—r, iv—s
• B. i—q, ii—r, iii—p, iv—s
• C. i—s, ii—p, iii—q, iv—r
• D. i—p, ii—r, iii—q, iv—s

Answer 1

Answer: (B)

(P) Forces are conservative so $E$ is constant, $KE$ will increase upto equilibrium and then decrease.
(q) Gravitation force is conservative, so $E$ is constant, $U$ decreases and $KE$ increases
$U=m g v-\frac{1}{2} m v^{2}$
$=\frac{1}{2} m(g t)^{2}$
(r) $U =$ mgh = constant; $E = U + KE$
$KE=-\frac{1}{2}mv^{2}$
$=\frac{1}{2}m\left(0+at\right)^{2}$
or $KE=-\frac{1}{2}m\left(\frac{F}{m}\times t\right)^{2}$
(s) Here velocity is constant, so $KE$ is constant.
As the block comes down $U$ decreases so $E$ decreases.