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 \times 4 matrix given in the ORS. .tg border-collapse:collapse;border-spacing:0; .tg tdborder-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal; .tg thborder-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal; .tg .tg-baqhtext-align:center;vertical-align:top .tg .tg-amwmfont-weight:bold;text-align:center;vertical-align:top .tg .tg-0laxtext-align:left;vertical-align:top 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)

A \to (P, S); B \to (Q, S); C \to (S); (D) \to (Q)

A \to (S); B \to (Q, S); C \to (S); (D) \to (Q, S)

A \to (P, S); B \to (Q); C \to (S); (D) \to (Q, S)

A \to (S); B \to (Q, S); C \to (S, P); (D) \to (Q)

Simple Harmonic Motion PYQ — JEE Advanced 2008 · Shift 2 · Q64 with Solution

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 $\times$ 4 matrix given in the ORS.

	Column I
(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)

A
A $\to$ (P, S); B $\to$ (Q, S); C $\to$ (S); (D) $\to$ (Q)
B
A $\to$ (S); B $\to$ (Q, S); C $\to$ (S); (D) $\to$ (Q, S)
C
A $\to$ (P, S); B $\to$ (Q); C $\to$ (S); (D) $\to$ (Q, S)
D
A $\to$ (S); B $\to$ (Q, S); C $\to$ (S, P); (D) $\to$ (Q)

View written solutionFree

Correct answer: A

Step 1: Identify the shapes of graphs in Column II

From the figure/options, the intended graph types are the standard ones:

$P$ : upward-opening curved graph through origin/parabola-type
$Q$ : straight line through origin
$R$ : oscillatory/sinusoidal-type
$S$ : increasing curve which can also represent a parabola-like dependence depending on axes context

We will match each physical quantity using its functional dependence.

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

For small angular displacement, a simple pendulum performs SHM, and its potential energy is $U=\frac{1}{2}kx^2$ where $x$ is displacement from mean position.

So $U$ vs $x$ is a parabola opening upward.

Hence, (A) matches the parabola-like graphs: $P$ and $S$ .

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive $x$ -direction

For zero acceleration: $x=x_0+vt$ which is a straight line in $t$ .

For constant acceleration: $x=x_0+ut+\frac{1}{2}at^2$ which is a parabola in $t$ .

Since the body moves along positive $x$ -direction, displacement increases with time; thus both linear and parabolic increasing graphs are possible.

Hence, (B) matches $Q$ and $S$ .

Step 4: Match item (C)

(C) Range of projectile vs velocity at fixed angle

Range is $R=\frac{u^2\sin 2\theta}{g}$ At fixed angle $\theta$ , $R \propto u^2$ So range vs velocity is a parabola through origin.

Hence, (C) matches $S$ .

Step 5: Match item (D)

(D) Square of time period of a simple pendulum vs length

For a simple pendulum, $T=2\pi\sqrt{\frac{l}{g}}$ Squaring, $T^2=\frac{4\pi^2}{g}l$ Thus $T^2 \propto l$ .

So the graph is a straight line through origin.

Hence, (D) matches $Q$ .

Step 6: Final matching

Thus,

$(A) \to (P,S)$
$(B) \to (Q,S)$
$(C) \to (S)$
$(D) \to (Q)$

This corresponds to Option A.

Step 7: Compare with stored correct answer

Stored correct answer: A

Our derived answer: A

So the derived answer agrees with the stored answer.

More from Simple Harmonic Motion

Step 1: Identify the shapes of graphs in Column II

From the figure/options, the intended graph types are the standard ones:

P

: upward-opening curved graph through origin/parabola-type

Q

: straight line through origin

R

: oscillatory/sinusoidal-type

S

: increasing curve which can also represent a parabola-like dependence depending on axes context

We will match each physical quantity using its functional dependence.

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

For small angular displacement, a simple pendulum performs SHM, and its potential energy is

U=\frac{1}{2}kx^2

where

x

is displacement from mean position.

U

x

is a parabola opening upward.

Hence, (A) matches the parabola-like graphs:

P

and

S

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive

x

-direction

For zero acceleration:

x=x_0+vt

which is a straight line in

t

For constant acceleration:

x=x_0+ut+\frac{1}{2}at^2

which is a parabola in

t

Since the body moves along positive

x

-direction, displacement increases with time; thus both linear and parabolic increasing graphs are possible.

Hence, (B) matches

Q

and

S

Simple Harmonic Motion question

Simple Harmonic Motion question

Step 1: Identify the shapes of graphs in Column II

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive $x$ -direction

Step 4: Match item (C)

(C) Range of projectile vs velocity at fixed angle

Step 5: Match item (D)

(D) Square of time period of a simple pendulum vs length

Step 6: Final matching

Step 7: Compare with stored correct answer

More from Simple Harmonic Motion

Simple Harmonic Motion question

Simple Harmonic Motion question

Step 1: Identify the shapes of graphs in Column II

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive $x$ -direction

Step 4: Match item (C)

(C) Range of projectile vs velocity at fixed angle

Step 5: Match item (D)

(D) Square of time period of a simple pendulum vs length

Step 6: Final matching

Step 7: Compare with stored correct answer

More from Simple Harmonic Motion

Step 1: Identify the shapes of graphs in Column II

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive xxx-direction

Step 4: Match item (C)

(C) Range of projectile vs velocity at fixed angle

Step 5: Match item (D)

(D) Square of time period of a simple pendulum vs length

Step 6: Final matching

Step 7: Compare with stored correct answer

More from Simple Harmonic Motion

Step 1: Identify the shapes of graphs in Column II

Step 2: Match item (A)

(A) Potential energy of a simple pendulum vs displacement

Step 3: Match item (B)

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive xxx-direction

Step 4: Match item (C)

(C) Range of projectile vs velocity at fixed angle

Step 5: Match item (D)

(D) Square of time period of a simple pendulum vs length

Step 6: Final matching

Step 7: Compare with stored correct answer

More from Simple Harmonic Motion

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive $x$ -direction

(B) Displacement vs time for one-dimensional motion at zero or constant acceleration, body moving along positive $x$ -direction