Physics || JEE Main previous year questions with Solutions

Q 1 :

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is _____. [2024]

$\frac{W}{2}$
$W$
$W$ $\cos$ $θ$
$W$ $\sin$ $θ$

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(1)

$N_{B} = net reaction force by shoulder.$

Balancing torque about point of contact $(A)$ on ground:

$W (\frac{L}{2} \cos θ) = N_{B} (L \cos θ)$

$\Rightarrow N_{B} = \frac{W}{2}$

Q 2 :

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the weight experienced by the man is _____. [2024]

6 kg
12 kg
3 kg
$6 \sqrt{3}$ kg

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(3)

$Torque about O = 0$

$120 (\frac{L}{2} \cos 60 °) - N_{2} L = 0$

$N_{2} = 30 N$

Q 3 :

The torque due to the force ( $2 \hat{i} + \hat{j} + 2 \hat{k}$ ) about the origin, acting on a particle whose position vector is ( $\hat{i} + \hat{j} + \hat{k}$ ), would be [2025]

( $\hat{i} - \hat{j} + \hat{k}$ )
( $\hat{i} + \hat{k}$ )
( $\hat{i} - \hat{k}$ )
( $\hat{j} - \hat{k}$ )

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(3)

$\vec{τ} = \vec{r} \times \vec{F}$

$\vec{τ} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 1 & 2 \end{matrix} |$

$\vec{τ} = \hat{i} (2 - 1) - \hat{j} [0] + \hat{k} (1 - 2) = \hat{i} - \hat{k}$

Q 4 :

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is [2025]

300 g
190 g
200 g
290 g

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(2)

$τ_{Net} = 0 \Rightarrow (400 g \times 30) = (250 g \times 10) + (m g \times 50)$

$m = \frac{12000 - 2500}{50} = \frac{9500}{50}$

$m = 190 g$

Q 5 :

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is: [2025]

20 N
0 (zero)
10 N
$10 \sqrt{2} N$

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(3)

Since the Lamina is equilibrium.

The net torque about O = 0

$- F l + 10 l - 10 l + 10 l = 0 \Rightarrow F = 10 N$

Q 6 :

Which of the following are correct expressions for torque acting on a body?

A. $\vec{τ} = \vec{r} \times \vec{L}$ B. $\vec{τ} = \frac{d}{d t} (\vec{r} \times \vec{p})$

C. $\vec{τ} = \vec{r} \times \frac{d \vec{p}}{d t}$ D. $\vec{τ} = I \vec{α}$

E. $\vec{τ} = \vec{r} \times \vec{F}$

( $\vec{r}$ = position vector; $\vec{p}$ = linear momentum; $\vec{L}$ = angular momentum;

$\vec{α}$ = angular acceleration; $I$ = moment of inertia; $\vec{F}$ = force; t = time)

Choose the correct answer from the options given below: [2025]

B, D and E Only
C and D Only
B, C, D and E Only
A, B, D and E Only

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(3)

$\vec{τ} = \vec{r} \times \vec{L}$ wrong

$\vec{τ} = \frac{d}{d t} (\vec{r} \times \vec{p})$ correct

$\vec{τ} = \vec{r} \times \frac{d \vec{p}}{d t} = \vec{r} \times \vec{F}$ correct

$\vec{τ} = I \vec{α}$ correct

$\vec{τ} = \vec{r} \times \vec{F}$ correct

Q 7 :

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

(2)

$\vec{τ} = \vec{r} \times \vec{F} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 1 & - 1 & 1 \end{matrix} |$

$\vec{τ} = \hat{k} (- 1 - 1) = - 2 \hat{k} \Rightarrow | \vec{τ} | = 2 Nm$

Q 8 :

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in fig. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 $m / s^{2}$ ) [2023]

240 N
30 N
300 N
90 N

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(3)

$System is in rotary equilibrium, \sum τ = 0 .$ $Taking torques about ' C'$

$T \sin 30 ° \times 60 = 20 \times 50 + 80 \times 100$

$T \times 30 = 1000 + 8000 = 9000$ $\Rightarrow T = 300 N$

Q 9 :

A force of $- P \hat{k}$ acts on the origin of the coordinate system. The torque about the point (2, - 3) is $P (a \hat{i} + b \hat{j})$ , the ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is _____ . [2023]

(3)

$τ = \vec{r} \times \vec{F}$

$Where \vec{r} = - 2 \hat{i} + 3 \hat{j}$

$τ = (- 2 \hat{i} + 3 \hat{j}) \times (- P \hat{k})$ $= P (- 2 \hat{j} - 3 \hat{i}) = P (- 3 \hat{i} - 2 \hat{j})$

$\Rightarrow So a = - 3, b = - 2$

$\frac{a}{b} = \frac{3}{2}$

Topic Question Set

Q 1 :

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is _____. [2024]

Q 2 :

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the weight experienced by the man is _____. [2024]

Q 3 :

The torque due to the force ( $2 \hat{i} + \hat{j} + 2 \hat{k}$ ) about the origin, acting on a particle whose position vector is ( $\hat{i} + \hat{j} + \hat{k}$ ), would be [2025]

Q 4 :

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is [2025]

Q 5 :

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is: [2025]

Q 7 :

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

Q 8 :

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in fig. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 $m / s^{2}$ ) [2023]

Q 9 :

A force of $- P \hat{k}$ acts on the origin of the coordinate system. The torque about the point (2, - 3) is $P (a \hat{i} + b \hat{j})$ , the ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is _____ . [2023]

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Topic Question Set

Q 1 : A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is _____. [2024]

Q 2 : A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the weight experienced by the man is _____. [2024]

Q 3 : The torque due to the force (2i^+j^+2k^) about the origin, acting on a particle whose position vector is (i^+j^+k^), would be [2025]

Q 4 : A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is [2025]

Q 5 : A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is: [2025]

Q 7 : The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of F→=i^–j^+k^ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

Q 8 : An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in fig. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s2) [2023]

Q 9 : A force of -Pk^ acts on the origin of the coordinate system. The torque about the point (2, - 3) is P(ai^+bj^), the ratio of ab is x2. The value of x is _____ . [2023]

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Q 1 :

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is _____. [2024]

Q 2 :

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the weight experienced by the man is _____. [2024]

Q 3 :

The torque due to the force ( $2 \hat{i} + \hat{j} + 2 \hat{k}$ ) about the origin, acting on a particle whose position vector is ( $\hat{i} + \hat{j} + \hat{k}$ ), would be [2025]

Q 4 :

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is [2025]

Q 5 :

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is: [2025]

Q 7 :

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

Q 8 :

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in fig. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 $m / s^{2}$ ) [2023]

Q 9 :

A force of $- P \hat{k}$ acts on the origin of the coordinate system. The torque about the point (2, - 3) is $P (a \hat{i} + b \hat{j})$ , the ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is _____ . [2023]