Match the Following, Potential energy of a simple pendulum (y axis) as a function of displacement (x axis) [2008]

Question

Match the Following [2008]

	Column I		Column II
(A)	Potential energy of a simple pendulum (y axis) as a function of displacement (x axis)	(p)
(B)	Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction.	(q)
(C)	Range of a projectile (y axis) as a function of its velocity (x axis) when projected at a fixed angle.	(r)
(D)	The square of the time period (y axis) of a simple pendulum as a function of its length (x axis)	(s)

Smart Achievers · Accepted Answer

(1)

(A) Potential energy is minimum at mean position and maximum at extreme position. In case of a S.H.M. we get a parabola for potential energy versus displacement graph.

(B) $S = u t$ for $a = 0$ . Therefore we get a straight line passing through the origin, as shown in graph (a).

If at $t = 0$ , $Y \neq 0$ and $Y = Y_{0}$ . Then for constant acceleration, we have graph as shown in (r).

$S = u t + \frac{1}{2} a t^{2}$ for constant positive acceleration. In this case we get a part of parabola as a graph line between $s$ versus $t$ as shown by graph (s).

(p) is ruled out because if $a$ is -ve and $v$ is positive.

$S = S_{0} + v t graph (r)$

$(C) : R = \frac{u^{2} \sin 2 θ}{g} \Rightarrow R \propto u^{2}$

$(D) : T = 2 π \sqrt{\frac{ℓ}{g}} \Rightarrow T^{2} \propto ℓ$

Solution

1 $A \to p; B \to q, r, s; C \to s; D \to q$

2 $A \to q, r, s; B \to p; C \to s; D \to q$

3 $A \to q, r, s; B \to p; C \to q; D \to s$

4 $A \to s; B \to p; C \to q; D \to q, r, s$

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Solution

1 A→p; B→q,r,s; C→s; D→q

2 A→q,r,s; B→p; C→s; D→q

3 A→q,r,s; B→p; C→q; D→s

4 A→s; B→p; C→q; D→q,r,s

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1 $A \to p; B \to q, r, s; C \to s; D \to q$

2 $A \to q, r, s; B \to p; C \to s; D \to q$

3 $A \to q, r, s; B \to p; C \to q; D \to s$

4 $A \to s; B \to p; C \to q; D \to q, r, s$