Back to Directory
NEET PHYSICSEasy

A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of aa. In the frame of the truck, the pendulum will tilt:

A

to the left and the angle of inclination of the pendulum with the vertical is sin⁡−1(ag)\sin^{-1}(\frac{a}{g})

B

to the left and the angle of inclination of the pendulum with the vertical is cos⁡−1(ag)\cos^{-1}(\frac{a}{g})

C

to the left and the angle of inclination of the pendulum with the vertical is tan⁡−1(ag)\tan^{-1}(\frac{a}{g})

D

to the left and the angle of inclination of the pendulum with the vertical is tan⁡−1(ga)\tan^{-1}(\frac{g}{a})

Step-by-Step Solution

  1. Frame of Reference: The problem asks for the behavior in the frame of the truck. Since the truck is accelerating to the right with acceleration aa, it constitutes a non-inertial frame of reference.
  2. Pseudo Force: In a non-inertial frame accelerating with a⃗\vec{a}, a pseudo force (fictitious force) acts on a particle of mass mm given by F⃗pseudo=−ma⃗\vec{F}_{pseudo} = -m\vec{a}. Since the truck accelerates to the right, the pseudo force acts on the bob to the left with magnitude mama.
  3. Forces on the Bob:
  • Weight (mgmg) acting vertically downwards.
  • Tension (TT) acting along the string.
  • Pseudo force (mama) acting horizontally to the left.
  1. Equilibrium: The bob comes to equilibrium at an angle θ\theta with the vertical where the net force is zero. Resolving forces:
  • Horizontal: Tsin⁡θ=maT \sin \theta = ma
  • Vertical: Tcos⁡θ=mgT \cos \theta = mg
  1. Calculating Angle: Dividing the horizontal equation by the vertical equation: Tsin⁡θTcos⁡θ=mamg\frac{T \sin \theta}{T \cos \theta} = \frac{ma}{mg} tan⁡θ=ag  ⟹  θ=tan⁡−1(ag)\tan \theta = \frac{a}{g} \implies \theta = \tan^{-1}\left(\frac{a}{g}\right) Thus, the pendulum tilts to the left with an angle tan⁡−1(a/g)\tan^{-1}(a/g). (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, concepts of equilibrium and non-inertial frames).
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started