JEE Advanced 2018 · Paper 1 · Physics Q2

← JEE Advanced 2018 · Paper 1

PhysicsMultiple correct+4 / -2Question 2 of 54

Consider a body of mass 1.0 kg at rest at the origin at time $t = 0$ . A force $\vec F = (\alpha t\,\hat i + \beta\,\hat j)$ is applied on the body, where $\alpha = 1.0\ \mathrm{N\,s^{-1}}$ and $\beta = 1.0$ N. The torque acting on the body about the origin at time $t = 1.0$ s is $\vec\tau$ . Which of the following statements is (are) true?

|\vec\tau| = \frac13

N m

The torque

\vec\tau

is in the direction of the unit vector

+\hat k

The velocity of the body at

t = 1

s is

\vec v = \frac12(\hat i + 2\hat j)\ \mathrm{m\,s^{-1}}

The magnitude of displacement of the body at

t = 1

s is

\frac16

Answer and worked solution

Official answer: A, C

With $m=1$ kg, $\vec a=\vec F=(t,\,1)$ .

Velocity. $\vec v=\left(\dfrac{t^2}2,\,t\right)$ , so at $t=1$ : $\vec v=\left(\tfrac12,1\right)=\tfrac12(\hat i+2\hat j)$ . (C) is true.

Position. $\vec r=\left(\dfrac{t^3}6,\,\dfrac{t^2}2\right)$ , so at $t=1$ : $\vec r=\left(\tfrac16,\tfrac12\right)$ . Its magnitude is $\dfrac{\sqrt{10}}6$ , not $\tfrac16$ . (D) is false.

Torque. At $t=1$ , $\vec F=(1,1)$ :
$\vec\tau=\vec r\times\vec F=\left(\tfrac16\cdot1-\tfrac12\cdot1\right)\hat k=-\tfrac13\hat k.$
So $|\vec\tau|=\tfrac13$ N m (A true), and it points along $-\hat k$ (B false).

(A), (C)

Topics:Torque and rotational dynamics Motion in a plane Newton's laws

← Previous question Next question →

JEE Advanced 2018 · Paper 1, Physics question 2