A particle of mass m is moving along a trajectory given by x = x _ 0 + acos ω _ 1 t y = y _ 0 + bsin ω _ 2 t The torque, acting on the particle about the origin, at t = 0 is:

Correct answer: A. + m y _ 0 a ω _ 1 ^ 2 ^ k x = x _ 0 + acos( ω _ 1 t) y = y _ 0 + bsin( ω _ 2 t) a _ x = - a ω _ 1 ^ 2 ( ω _ 1 t) a _ y = - b ω _ 2 ^ 2 ( ω _ 2 t) At t = 0 , → F = m → a = (- a ω _ 1 ^ 2 ^ i ) And → r = ( x _ 0 +a) ^ i + y _ 0 ^ j Torque, τ = → r × → F τ = (( x _ 0 +a) ^ i + y _ 0 ^ j ) × (- a ω _ 1 ^ 2 ^ i ) = m y _ 0 a ω _ 1 ^ 2 ^ k

JEE Main 201910 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 April
Shift: Morning Shift
Subject: Physics
Chapter: Motion in Two Dimensions

JEE Main 2019 · 10 April · Morning Shift · Physics · Motion in Two Dimensions

A particle of mass m is moving along a trajectory given by x = x _...

A particle of mass

m

is moving along a trajectory given by

x = {x}_{0} + acos{\omega}_{1}t

y = {y}_{0} + bsin{\omega}_{2}t

The torque, acting on the particle about the origin, at

t = 0

is:

Options

A $+ m{y}_{0}a{\omega}_{1}^{2}\overset{^}{k}$
B- m $\left({x}_{0}b{\omega}_{2}^{2} - {y}_{0}a{\omega}_{1}^{2}\right)\overset{^}{k}$
CZero
D $m\left(- {x}_{0}b + {y}_{0}a\right){\omega}_{1}^{2}\overset{^}{k}$

Correct answer

A. $+ m{y}_{0}a{\omega}_{1}^{2}\overset{^}{k}$

Step-by-step solution

x = {x}_{0} + acos\left({\omega}_{1}t\right)

y = {y}_{0} + bsin\left({\omega}_{2}t\right)

{a}_{x} = - a{\omega}_{1}^{2}\cos \left({\omega}_{1}t\right)

{a}_{y} = - b{\omega}_{2}^{2}\sin \left({\omega}_{2}t\right)

t = 0

\overset{\to}{F} = m\overset{\to}{a} = \left(- a{\omega}_{1}^{2}\overset{^}{i}\right)

And

\overset{\to}{r} = \left({x}_{0}\text{+}a\right)\overset{^}{i} + {y}_{0}\overset{^}{j}

Torque,

τ = \overset{\to}{r} \times \overset{\to}{F}

τ = \left(\left({x}_{0}\text{+}a\right)\overset{^}{i} + {y}_{0}\overset{^}{j}\right) \times \left(- a{\omega}_{1}^{2}\overset{^}{i}\right)

= m{y}_{0}a{\omega}_{1}^{2}\overset{^}{k}

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026 A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026 Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026 If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026 A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026 Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026 A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026 An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Main PYQs