Two simple pendulums having lengths and with negligible string mass undergo angular displacements and , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct? [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $θ_{1}$ and $θ_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct [2025]

1 $θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$

2 $θ_{1} l_{1} = θ_{2} l_{2}$

3 $θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$

4 $θ_{1} l_{2} = θ_{2} l_{1}$

Ans.
(4)

Angular frequency of simple pendulum, $ω = \sqrt{\frac{g}{l}}$

Angular acceleration, $α = - ω^{2} θ$

$∴ \frac{g}{l_{1}} θ_{1} = \frac{g}{l_{2}} θ_{2}$

$\Rightarrow θ_{1} l_{2} = θ_{2} l_{1}$

Solution

Q.
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $θ_{1}$ and $θ_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct [2025]

1 $θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$

2 $θ_{1} l_{1} = θ_{2} l_{2}$

3 $θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$

4 $θ_{1} l_{2} = θ_{2} l_{1}$

Ans.
(4)

Angular frequency of simple pendulum, $ω = \sqrt{\frac{g}{l}}$

Angular acceleration, $α = - ω^{2} θ$

$∴ \frac{g}{l_{1}} θ_{1} = \frac{g}{l_{2}} θ_{2}$

$\Rightarrow θ_{1} l_{2} = θ_{2} l_{1}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Two simple pendulums having lengths l1 and l2 with negligible string mass undergo angular displacements θ1 and θ2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct [2025]

1 θ1l22=θ2l12

2 θ1l1=θ2l2

3 θ1l12=θ2l22

4 θ1l2=θ2l1

Ans. (4) Angular frequency of simple pendulum, ω=gl Angular acceleration, α=–ω2θ ∴ gl1θ1=gl2θ2 ⇒ θ1l2=θ2l1

Want Us to Email you About Special Offers & Updates?

Q.
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $θ_{1}$ and $θ_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct [2025]

1 $θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$

2 $θ_{1} l_{1} = θ_{2} l_{2}$

3 $θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$

4 $θ_{1} l_{2} = θ_{2} l_{1}$

Ans.
(4)

Angular frequency of simple pendulum, $ω = \sqrt{\frac{g}{l}}$

Angular acceleration, $α = - ω^{2} θ$

$∴ \frac{g}{l_{1}} θ_{1} = \frac{g}{l_{2}} θ_{2}$

$\Rightarrow θ_{1} l_{2} = θ_{2} l_{1}$