You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Elastic Potential Energy

A bob of mass...

Question

A bob of mass $m$ is suspended from the ceiling of a train moving with an acceleration $a$ as shown in figure. Find the angle $θ$ in equilibrium position.

t a n^{- 1} \frac{a}{g}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

t a n^{- 1} \frac{g}{a}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

c o t^{- 1} \frac{a + g}{a - g}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $t a n^{- 1} \frac{a}{g}$
From the frame of reference of train, there is pseudo force of $m a$ on bob in backward direction.
Balancing force in horizontal direction, $T s i n θ = m a$
Balancing force in vertical direction, $T c o s θ = m g$
Taking ratio, $\frac{s i n θ}{c o s θ} = \frac{a}{g}$
$⟹ t a n θ = \frac{a}{g} ⟹ θ = t a n^{- 1} \frac{a}{g}$

Suggest Corrections

Similar questions

Q. A bob of mass m is suspended from the ceiling of a train moving with an acceleration a as shown in figure. Find the angle

θ

in equilibrium position.

Q. A pendulum of mass

m

and length

l

is suspended from the ceiling of a trolley which has a constant acceleration

a

. The maximum deflection

θ

of the pendulum from the vertical is

A pendulum of mass m as hanging from the ceiling of a car having an acceleration $a_{0}$ with respect to the road. Find the angle made by the string with the vertical.

Q. A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration 'a' along a straight horizontal track , the string supporting the bob makes an angle tan⁻¹ (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan⁻¹ (a/g), the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerating on a horizontal straight track or moving on an incline? If yes, how? If not, then suggest a method to do so.

Q. A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination

30^{\circ}

with horizontal. Acceleration of train up the plane is

a = \frac{g}{2}

. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is

θ

. Then

tan θ

upto 2 decimal places is

Join BYJU'S Learning Program

A bob of mass m is suspended from the ceiling of a train moving with an acceleration a as shown in figure. Find the angle θ in equilibrium position.

The correct option is A tan−1agFrom the frame of reference of train, there is pseudo force of ma on bob in backward direction.Balancing force in horizontal direction, Tsinθ=maBalancing force in vertical direction, Tcosθ=mgTaking ratio, sinθcosθ=ag⟹tanθ=ag⟹θ=tan−1ag

A bob of mass $m$ is suspended from the ceiling of a train moving with an acceleration $a$ as shown in figure. Find the angle $θ$ in equilibrium position.