JEE Advanced 2021 · Paper 1 · Physics Q13

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PhysicsMultiple correct+4 / -2Question 13 of 57

A particle of mass $M = 0.2$ kg is initially at rest in the $xy$ -plane at a point $(x = -l, y = -h)$ , where $l = 10$ m and $h = 1$ m. The particle is accelerated at time $t = 0$ with a constant acceleration $a = 10\ \text{m/s}^2$ along the positive $x$ -direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec L$ and $\vec\tau$ , respectively. $\hat i$ , $\hat j$ and $\hat k$ are unit vectors along the positive $x$ , $y$ and $z$ -directions, respectively. If $\hat k = \hat i \times \hat j$ then which of the following statement(s) is(are) correct?

The particle arrives at the point

(x = l, y = -h)

at time

t = 2

\vec\tau = 2\hat k

when the particle passes through the point

(x = l, y = -h)

\vec L = 4\hat k

when the particle passes through the point

(x = l, y = -h)

\vec\tau = \hat k

when the particle passes through the point

(x = 0, y = -h)

Answer and worked solution

Official answer: A, B, C

Motion. $x=-10+5t^2$ , so the particle reaches $x=10$ when $5t^2=20$ , i.e. $t=2$ s. (A) is true.

At $(l,-h)$ . Here $\vec r=10\hat i-\hat j$ , $\vec v=20\hat i$ and $\vec p=4\hat i$ (in kg m/s). The force is $\vec F=Ma\,\hat i=2\hat i$ N.

$\vec\tau=\vec r\times\vec F=(-\hat j)\times2\hat i=2\hat k$ . (B) is true.
$\vec L=\vec r\times\vec p=(-\hat j)\times4\hat i=4\hat k$ . (C) is true.

At $(0,-h)$ . $\vec\tau=(-\hat j)\times2\hat i=2\hat k$ , not $\hat k$ . (D) is false.

(A), (B), (C)

Topics:Angular momentum and its conservation Torque and rotational dynamics Motion in a straight line

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JEE Advanced 2021 · Paper 1, Physics question 13