Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the

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Q.
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reasosn (R) : The mass of the pendulum remains unchanged at Earth and the other planet.

In the light of the above statements, choose the correct answer from the options given below: [2025]

1 Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

2 (A) is true but (R) is false.

3 (A) is false but (R) is true.

4 Both (A) and (R) are true and (R) is the correct explanation of (A).

Ans.
(1)

$g = \frac{G M}{R^{2}}$

$g' = \frac{G (4 M)}{{(2 R)}^{2}} = g$

A is correct, R is correct; but since $T = 2 π \sqrt{\frac{l}{g}}$

Doesn't depend on mass; R doesn't explain A.

Solution

1 Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

2 (A) is true but (R) is false.

3 (A) is false but (R) is true.

4 Both (A) and (R) are true and (R) is the correct explanation of (A).

Ans.
(1)

$g = \frac{G M}{R^{2}}$

$g' = \frac{G (4 M)}{{(2 R)}^{2}} = g$

A is correct, R is correct; but since $T = 2 π \sqrt{\frac{l}{g}}$

Doesn't depend on mass; R doesn't explain A.

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Solution

1 Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

2 (A) is true but (R) is false.

3 (A) is false but (R) is true.

4 Both (A) and (R) are true and (R) is the correct explanation of (A).

Ans. (1) g=GMR2 g'=G(4M)(2R)2=g A is correct, R is correct; but since T=2πlg Doesn't depend on mass; R doesn't explain A.

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Ans.
(1)

$g = \frac{G M}{R^{2}}$

$g' = \frac{G (4 M)}{{(2 R)}^{2}} = g$

A is correct, R is correct; but since $T = 2 π \sqrt{\frac{l}{g}}$

Doesn't depend on mass; R doesn't explain A.