Impulse and Momentum questions | Impulse and Momentum jee questions

Q 1 :

A particle moves in $x - y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p} (t) = \hat{i} \cos (k t) - \hat{j} \sin (k t) .$ If $k$ is constant, the angle between $\vec{F}$ and $\vec{p}$ will be [2024]

$\frac{π}{2}$
$\frac{π}{4}$
$\frac{π}{3}$
$\frac{π}{6}$

1

2

3

4

(1)

$\frac{π}{2}$

Q 2 :

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1s, the magnitude of force exerted by the ball on the hand of the player is [2024]

150 N
3 N
30 N
300 N

1

2

3

4

(3) 30 N

Q 3 :

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) [2024]

24
12
25
30

1

2

3

4

(4) 30

Q 4 :

Figures a, b, c and d show variation of force with time.

[IMAGE 18]

The impulse is highest in figure. [2023]

Fig (c)
Fig (b)
Fig (a)
Fig (d)

1

2

3

4

(2)

$Impulse = Area under F = t curve$

$(a) \frac{1}{2} \times 1 \times 0.5 = \frac{1}{4} N·s$

$(b) 0.5 \times 2 = 1 N·s (maximum)$

$(c) \frac{1}{2} \times 1 \times 0.75 = \frac{3}{8} N·s$

$(d) \frac{1}{2} \times 2 \times 0.5 = \frac{1}{2} N·s$

Q 5 :

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is [2023]

5
50
100
25

1

2

3

4

(2)

$F = n m v$

$where n = number of bullets fired per second$

$n = \frac{F}{m v} = \frac{125}{10 \times 10^{- 3} \times 250} = 50$

Q 6 :

A body of mass 500 g moves along the $x$ -axis such that its velocity varies with displacement $x$ according to the relation $v = 10 \sqrt{x}$ m/s. The force acting on the body is [2023]

166 N
25 N
125 N
5 N

1

2

3

4

(2)

$v = 10 \sqrt{x} \Rightarrow v^{2} = 100 x$

$2 v \frac{d v}{d x} = 100 \Rightarrow a = 50 {m/s}^{2}$

$Hence, F = 25 N$

Q 7 :

Three forces $F_{1} = 10 N$ , $F_{2} = 8 N$ , $F_{3} = 6 N$ are acting on a particle of mass 5 kg. The forces $F_{2}$ and $F_{3}$ are applied perpendicular so that the particle remains at rest. If the force $F_{1}$ is removed, then the acceleration of the particle is [2023]

$2 {m s}^{- 2}$
$0.5 {m s}^{- 2}$
$4.8 {m s}^{- 2}$
${7 m s}^{- 2}$

1

2

3

4

(1)

$Resultant of {\vec{F}}_{2} and {\vec{F}}_{3} should be opposite to {\vec{F}}_{1}$

$a = \frac{10}{5} = 2 {m/s}^{2}$

Q 8 :

A bullet of 10 g leaves the barrel of a gun with a velocity of 600 m/s. If the barrel of the gun is 50 cm long and the mass of the gun is 3 kg, then the value of impulse supplied to the gun will be [2023]

12 Ns
6 Ns
36 Ns
3 Ns

1

2

3

4

(2)

$By momentum conservation$

$0 = 3 (- v) + 0.01 (600 - v)$

$v = 2 m/s$

Impulse on gun = $3 \times 2 = 6 Ns$

Topic Question Set

Q 1 :

A particle moves in $x - y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p} (t) = \hat{i} \cos (k t) - \hat{j} \sin (k t) .$ If $k$ is constant, the angle between $\vec{F}$ and $\vec{p}$ will be [2024]

Q 2 :

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1s, the magnitude of force exerted by the ball on the hand of the player is [2024]

Q 3 :

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) [2024]

Q 4 :

Figures a, b, c and d show variation of force with time.

[IMAGE 18]

The impulse is highest in figure. [2023]

Q 5 :

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is [2023]

Q 6 :

A body of mass 500 g moves along the $x$ -axis such that its velocity varies with displacement $x$ according to the relation $v = 10 \sqrt{x}$ m/s. The force acting on the body is [2023]

Q 7 :

Three forces $F_{1} = 10 N$ , $F_{2} = 8 N$ , $F_{3} = 6 N$ are acting on a particle of mass 5 kg. The forces $F_{2}$ and $F_{3}$ are applied perpendicular so that the particle remains at rest. If the force $F_{1}$ is removed, then the acceleration of the particle is [2023]

Q 8 :

A bullet of 10 g leaves the barrel of a gun with a velocity of 600 m/s. If the barrel of the gun is 50 cm long and the mass of the gun is 3 kg, then the value of impulse supplied to the gun will be [2023]

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