Question

Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the $4 	imes 4$ matrix given in the ORS.

| Column I | Column II |
| --- | --- |
| (A) Potential energy of a simple pendulum ($y$ axis) as a function of displacement ($x$ axis) | (p) (see structure) |
| (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) (see structure) |
| (C) Range of a projectile ($y$ axis) as a function of its velocity ($x$ axis) when projected at a fixed angle | (r) (see structure) |
| (D) The square of the time period ($y$ axis) of a simple pendulum as a function of its length ($x$ axis) | (s) (see structure) |

Accepted Answer

Matching based on the nature of graphs:

(A) → (s): Potential energy of a pendulum varies as

P E \propto x^{2}

(parabolic)

(B) → (q) & (s): For constant velocity, displacement vs time is linear (q). For constant acceleration, it's parabolic (s).

(C) → (s): Range

R = \frac{v ^{2} s i n ( 2 θ )}{g}

, so

R \propto v^{2}

(parabolic)

(D) → (q):

T^{2} = \frac{4 π ^{2}}{g} L

, so

T^{2} \propto L

(linear)

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Elasticity & SHM

Solution

More JEE Advanced questions on Elasticity & SHM

Column I	Column II
(A) Potential energy of a simple pendulum ( $y$ axis) as a function of displacement ( $x$ axis)	(p) (see structure)
(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) (see structure)
(C) Range of a projectile ( $y$ axis) as a function of its velocity ( $x$ axis) when projected at a fixed angle	(r) (see structure)
(D) The square of the time period ( $y$ axis) of a simple pendulum as a function of its length ( $x$ axis)	(s) (see structure)