The position vector of 1 kg object is $\overrightarrow{\mathrm{r}}=(3 \hat{\mathrm{i}}-\hat{\mathrm{j}}) \mathrm{m}$ and its velocity $\overrightarrow{\mathrm{v}}=(3 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \mathrm{ms}^{-1}$. The magnitude of its angular momentum is $\sqrt{\mathrm{x}} \mathrm{Nm}$ where x is \_\_\_\_.

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Rotational Mechanics

The position vector of 1 kg object is

r = (3 \hat{i} - \hat{j}) m

and its velocity

v = (3 \hat{j} + \hat{k}) ms^{- 1}

. The magnitude of its angular momentum is

x Nm

where x is ____.

Answer: 91

Solution

Angular momentum is given by

L = r \times m v

. With

m = 1

kg, we have

L = (3 \hat{i} - \hat{j}) \times (3 \hat{j} + \hat{k})

. Expanding the cross product:

L = 3 \hat{i} \times 3 \hat{j} + 3 \hat{i} \times \hat{k} - \hat{j} \times 3 \hat{j} - \hat{j} \times \hat{k} = 9 \hat{k} - 3 \hat{i} - 0 - (- \hat{i}) = - \hat{i} - 3 \hat{j} + 9 \hat{k}

. The magnitude is

∣ L ∣ = 1 + 9 + 81 = 91

N·m. Therefore,

x = 91

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Rotational Mechanics →

More JEE Main questions on Rotational Mechanics

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ______ kg.m².
JEE Main 2026View solution →
A circular disc has radius $R_{1}$ and thickness $T_{1}$ . Another circular disc made of the same material has radius $R_{2}$ and thickness $T_{2}$ . If the moment of inertia of both discs are same and $\frac{R _{1}}{R _{2}} = 2$ then $\frac{T _{1}}{T _{2}} = \frac{1}{α}$ . …
JEE Main 2026View solution →
Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius $r = 0.1 m$ . The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended thr …
JEE Main 2026View solution →
Two cars A and B each of mass $1 0^{3} kg$ are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds $72 km / h$ and $36 km / h$ . The magnitude of angular momentum of car A with respect to ca …
JEE Main 2026View solution →
The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in v …
JEE Main 2026View solution →
The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length $L$ ( $R < L$ ) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M):
JEE Main 2026View solution →