A trolley moves in horizontal direction with an acceleration a. A simple pendulum of length l is suspended from the roof of the trolley. The time period of the pendulum will be

Question

A trolley moves in horizontal direction with an acceleration a. A simple pendulum of length l is suspended from the roof of the trolley. The time period of the pendulum will be (A) infinity (B) zero (C) 2 π √(l/(g+a)) (D) 2 π √(l/√a2+g2)

Tardigrade Admin · Accepted Answer

Two accelerations are acting on the bob of pendulum.
(i) Vertically downwards, acceleration

= g

(ii) Horizontally, due to acceleration of trolley

= a

.
Effective acceleration

= g^{2} + a^{2}

∴ T = 2 π \frac{l}{g ^{2} + a ^{2}}

Q. A trolley moves in horizontal direction with an acceleration a. A simple pendulum of length l is suspended from the roof of the trolley. The time period of the pendulum will be

infinity

zero

$2 π \frac{l}{( g + a )}$

$2 π \frac{l}{a ^{2} + g ^{2}}$

Two accelerations are acting on the bob of pendulum.
(i) Vertically downwards, acceleration $= g$
(ii) Horizontally, due to acceleration of trolley $= a$ .
Effective acceleration $= g^{2} + a^{2}$
$∴ T = 2 π \frac{l}{g ^{2} + a ^{2}}$

Q. A trolley moves in horizontal direction with an acceleration a. A simple pendulum of length l is suspended from the roof of the trolley. The time period of the pendulum will be

infinity

zero

2π(g+a)l​​

2πa2+g2​l​​

Two accelerations are acting on the bob of pendulum. (i) Vertically downwards, acceleration =g (ii) Horizontally, due to acceleration of trolley =a. Effective acceleration =g2+a2​ ∴T=2πg2+a2​l​​

$2 π \frac{l}{( g + a )}$

$2 π \frac{l}{a ^{2} + g ^{2}}$

Two accelerations are acting on the bob of pendulum.
(i) Vertically downwards, acceleration $= g$
(ii) Horizontally, due to acceleration of trolley $= a$ .
Effective acceleration $= g^{2} + a^{2}$
$∴ T = 2 π \frac{l}{g ^{2} + a ^{2}}$