Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202628 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Evening Shift
Subject
Physics
Chapter
Laws of Motion

JEE Main 2026 · 28 January · Evening Shift · Physics · Laws of Motion

A small block of mass m slides down from the top of a frictionless...

A small block of mass mm slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration a0a_{0}. The angle between the inclined plane and ground is θ\theta and its base length is LL. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ____\_\_\_\_.
A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving

Options

  1. A2Lgsin⁡θ−a0cos⁡θ\sqrt{\frac{2 L}{g \sin \theta-a_{0} \cos \theta}}
  2. B4Lgcos⁡2θ−a0sin⁡θcos⁡θ\sqrt{\frac{4 L}{g \cos ^{2} \theta-a_{0} \sin \theta \cos \theta}}
  3. C2Lgsin⁡2θ−a0(1+cos⁡2θ)\sqrt{\frac{2 L}{g \sin 2 \theta-a_{0}(1+\cos 2 \theta)}}
  4. D4Lgsin⁡2θ−a0(1+cos⁡2θ)\sqrt{\frac{4 L}{g \sin 2 \theta-a_{0}(1+\cos 2 \theta)}}

Correct answer

D. 4Lgsin⁡2θ−a0(1+cos⁡2θ)\sqrt{\frac{4 L}{g \sin 2 \theta-a_{0}(1+\cos 2 \theta)}}

Step-by-step solution

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving
mgsin⁡θ−ma0cos⁡θ=mamg\sin\theta - ma_0\cos\theta = ma
a=gsin⁡θ−a0cos⁡θa = g\sin\theta - a_0\cos\theta
Now using,
S=ut+12adownt2S = ut + \dfrac{1}{2}a_{down}t^2
Lcos⁡θ=12(gsin⁡θ−a0cos⁡θ)t2\dfrac{L}{\cos\theta} = \dfrac{1}{2}(g\sin\theta - a_0\cos\theta)t^2
t=2Lgsin⁡θcos⁡θ−a0cos⁡2θt = \sqrt{\dfrac{2L}{g\sin\theta\cos\theta - a_0\cos^2\theta}}
t=4Lgsin⁡2θ−a0(1+cos⁡2θ)t = \sqrt{\dfrac{4L}{g\sin 2\theta - a_0(1 + \cos 2\theta)}}
Practice Laws of Motion on Quantrex Academy →

More from Laws of Motion

A block takes t time to slide down a plane inclined at 45° to the horizontal. If the… JEE Main 2026Two blocks ( P and Q ) with respectively masses 2 kg and 1.5 kg are joined by a massless… JEE Main 2026A mass of 1 kg is kept on an inclined plane with 30° inclination with respect to… JEE Main 2026Three masses m_1 = 4 kg, m_2 = 4 kg and m_3 = 6 kg are suspended from a fixed smooth… JEE Main 2026A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface… JEE Main 2026At t=0 , a body of mass 100 g starts moving under the influence of a force (5 i +10 j )… JEE Main 2026The time taken by a block of mass m to slide down from the highest point to the lowest… JEE Main 2026A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m… JEE Main 2026 Full Laws of Motion list All JEE Main PYQs