Newton's Laws of Motion questions | Newton's Laws of Motion jee questions

Q 1 :

A body of mass 4 kg experiences two forces ${\vec{F}}_{1} = 5 \hat{i} + 8 \hat{j} + 7 \hat{k}$ and ${\vec{F}}_{2} = 3 \hat{i} - 4 \hat{j} - 3 \hat{k}$ . The acceleration acting on the body is [2024]

$- 2 \hat{i} - \hat{j} - \hat{k}$
$4 \hat{i} + 2 \hat{j} + 2 \hat{k}$
$2 \hat{i} + \hat{j} + \hat{k}$
$2 \hat{i} + 3 \hat{j} + 3 \hat{k}$

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(3)

$F_{n e t} = {\vec{F}}_{1} + {\vec{F}}_{2} = 8 \hat{i} + 4 \hat{j} + 4 \hat{k}$

$\frac{F_{n e t}}{m} = 2 \hat{i} + \hat{j} + \hat{k}$

Q 2 :

A wooden block, initially at rest on the ground, is pushed by a force that increases linearly with time t. Which of the following curves best describes the acceleration of the block with time? [2024]

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(2)

Let $F = k t$

$F = m a \Rightarrow a = \frac{F}{m} = (\frac{k}{m}) t$

It means the acceleration vs. time graph will be a straight line passing through the origin.

Q 3 :

A block of mass 1 kg, moving along x with speed $v_{i}$ = 10 m/s enters a rough region ranging from x = 0.1 m to x = 1.9 m. The retarding force acting on the block in this range is $F_{r}$ = – kx N, with k = 10 N/m. Then the final speed of the block as it crosses rough region is [2025]

10 m/s
4 m/s
6 m/s
8 m/s

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(4)

$a = \frac{F}{m} = - 10 x \Rightarrow v \frac{d v}{d x} = - 10 x$

$\int_{10}^{v} v d v = - 10 \int_{0.1}^{1.9} x d x$

$\frac{v^{2} - 100}{2} = - 10 (\frac{{(1.9)}^{2} - {(0.1)}^{2}}{2})$

$\Rightarrow v = 8 m / s$

Q 4 :

An object with mass 500 g moves along x-axis with speed $v = 4 \sqrt{x} m / s$ . The force acting on the object is : [2025]

8 N
5 N
6 N
4 N

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(4)

The force acting on the object, F = ma

$v = 4 \sqrt{x} \Rightarrow v^{2} = 16 x$

$2 v \frac{d v}{d x} = 16$

$a = v \frac{d v}{d x} = \frac{16}{2} = 8 {ms}^{- 2}$

$\Rightarrow F = 0.5 \times 8 = 4 N$

Q 5 :

A body of mass 2 kg moving with velocity of ${\vec{v}}_{i n} = 3 \hat{i} + 4 \hat{j} {ms}^{- 1}$ enters in to a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is [2025]

$4 \hat{i} + 3 \hat{j} + 5 \hat{k}$
$3 \hat{i} + 4 \hat{j} + 5 \hat{k}$
$3 \hat{i} + 4 \hat{j} - 5 \hat{k}$
$3 \hat{i} + 4 \hat{j} + \sqrt{5} \hat{k}$

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(2)

$\vec{a} = \frac{6}{2} (\hat{k}) {ms}^{- 2} = 3 (\hat{k}) {ms}^{- 2}, t = \frac{5}{3} s$

$\vec{u} = (3 \hat{i} + 4 \hat{j}) {ms}^{- 1}$

$\vec{v} = \vec{u} + \vec{a t} = (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) {ms}^{- 1}$

Q 6 :

Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be [2023]

40 N
5 N
20 N
10 N

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(2)

[IMAGE 17]

$50 = V \times 10 \Rightarrow V = 5 m/s$

$V = 0 + a \times 20$

$\Rightarrow 5 = a \times 20 \Rightarrow a = \frac{1}{4} {m/s}^{2}$

$F = m a = 20 \times \frac{1}{4} = 5 N$

Q 7 :

At any instant the velocity of a particle of mass 500 g is $(2 t \hat{i} + 3 t^{2} \hat{j}) {m s}^{- 1} .$ If the force acting on the particle at $t$ = 1 s is $(\hat{i} + x \hat{j}) N,$ then the value of $x$ will be [2023]

3
6
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4

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(1)

$\vec{v} = 2 t \hat{i} + 3 t^{2} \hat{j}$

$\vec{a} = 2 \hat{i} + 6 t \hat{j}$

$At t = 1, \vec{a} = 2 \hat{i} + 6 \hat{j}$

$\vec{F} = m \vec{a} = 0.5 (2 \hat{i} + 6 \hat{j}) = \hat{i} + 3 \hat{j}$

$\vec{F} = \hat{i} + x \hat{j}$

Hence $x$ = 3

Q 8 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: An electric fan continues to rotate for some time after the current is switched off.

Reason R: Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below. [2023]

A is correct but R is not correct.
Both A and R are correct and R is the correct explanation of A.
A is not correct but R is correct.
Both A and R are correct but R is NOT the correct explanation of A.

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(2)

Fan continue to rotate due to inertia of motion.

Q 9 :

The position vector of a particle related to time $t$ is given by $\hat{r} = (10 t \hat{i} + 15 t^{2} \hat{j} + 7 \hat{k}) m$

The direction of net force experienced by the particle is [2023]

Positive y-axis
Positive $x$ -axis
Positive z-axis
In $x - y$ plane

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(1)

$\hat{r} = 10 t \hat{i} + 15 t \hat{j} + 7 \hat{k}$

$\vec{v} = 10 \hat{i} + 30 t \hat{j}$

$\vec{a} = 30 \hat{j}$

$So, net force is along the + y direction.$

Topic Question Set

Q 1 :

A body of mass 4 kg experiences two forces ${\vec{F}}_{1} = 5 \hat{i} + 8 \hat{j} + 7 \hat{k}$ and ${\vec{F}}_{2} = 3 \hat{i} - 4 \hat{j} - 3 \hat{k}$ . The acceleration acting on the body is [2024]

Q 2 :

A wooden block, initially at rest on the ground, is pushed by a force that increases linearly with time t. Which of the following curves best describes the acceleration of the block with time? [2024]

Q 3 :

A block of mass 1 kg, moving along x with speed $v_{i}$ = 10 m/s enters a rough region ranging from x = 0.1 m to x = 1.9 m. The retarding force acting on the block in this range is $F_{r}$ = – kx N, with k = 10 N/m. Then the final speed of the block as it crosses rough region is [2025]

Q 4 :

An object with mass 500 g moves along x-axis with speed $v = 4 \sqrt{x} m / s$ . The force acting on the object is : [2025]

Q 6 :

Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be [2023]

Q 7 :

At any instant the velocity of a particle of mass 500 g is $(2 t \hat{i} + 3 t^{2} \hat{j}) {m s}^{- 1} .$ If the force acting on the particle at $t$ = 1 s is $(\hat{i} + x \hat{j}) N,$ then the value of $x$ will be [2023]

Q 9 :

The position vector of a particle related to time $t$ is given by $\hat{r} = (10 t \hat{i} + 15 t^{2} \hat{j} + 7 \hat{k}) m$

The direction of net force experienced by the particle is [2023]

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