A particle moving in the xy -plane experiences a velocity dependent force F → = k υ y i ^ + υ x j ^ , where υ x and υ y are the x and y components of its velocity υ → . If a → is the acceleration of the particle, then which of the following statements is true for the particle ?

quantity υ → × a → is constant in time

F → arises due to a magnetic field

kinetic energy of particle is constant in time

quantity υ → . a → is constant in time

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Two masses $M_{1}$ and $M_{2}$ are arranged as shown in the figure. Let ' $a$ ' be the magnitude of the acceleration of the mass $M_{1}$ . If the mass of $M_{1}$ is doubled and that of $M_{2}$ is halved, then the acceleration of the system is
(Treat all surfaces as smooth : masses of pulley and rope are negligible )

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Important Questions on Laws of Motion

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

The time taken by a force of

2 N

to produce a change of momentum of

0.4 kg m s^{- 1}

in a

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A body of mass

m

is moving in a straight line with momentum

p

. Starting at time

t = 0

, a force

F = a t

acts in the same direction on the moving particle during time interval of

T

. So that its momentum changes from

p

2 p

. The value of

T

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A steam of water flowing horizontally with a speed of

25 {ms}^{- 1}

gushes out of a tube of cross-section area

10^{- 3} m^{2}

, and hits at a vertical wall nearby. What is the force exerted on the wall by the impact of water ?

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A force of

0.03 N

acts on a body of mass

0.5 kg

, which is initially at rest, for a duration of

10

seconds. Then find the momentum acquired by the body.

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A force of

(2 \hat{i} + 3 \hat{j}) N

acts on a body of mass

1 kg

which is at rest initially. The acceleration of the body is

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

The pair with same dimension is ___.

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

The force on a body of mass

1 kg

(20 \hat{i} + 10 \hat{j}) N

. If it starts from rest, then the position of the body at time

t = 2 s,

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

The velocity

(v)

of a particle

(

under a force

F)

depends on its distance

(x)

from the origin (with

x > 0

)

v \propto \frac{1}{\sqrt{x}}

. Find how the magnitude of the force

(F)

on the particle depends on

x ?

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A body of mass

2 kg

is moving with a momentum of

10 kg {ms}^{- 1} .

The force needed to increase its kinetic energy by four times in

10

seconds is

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A machine gun has a mass

5 kg

. It fires

50

gram bullets at the rate of

30

bullets per minute at a speed of

400 m s^{- 1} .

What force is required to keep the gun in position?

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A machine gun can fire

200 bullets \min^{- 1}

. If

35 g

bullets are fired at a speed of

750 m s^{- 1}

, the average force exerted by the gun on the bullets is,

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A ball is thrown upward with an initial velocity

V_{0}

from the surface of the earth. The motion of the ball is affected by a drag force equal to

m γ v^{2}

(where

m

is mass of the ball,

v

is its instantaneous velocity and

γ

is a constant). Time taken by the ball to rise to its zenith is:

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

Two horizontal forces

{\vec{F}}_{1}

and

{\vec{F}}_{2}

act on a ball of mass

8 kg

. The forces are such that

{\vec{F}}_{1} = (14 N) \hat{i}

and

|{\vec{F}}_{2}| = 20 N

. If the

x

component of velocity

(v_{x})

changes linearly by

3 m s^{- 1}

1 \sec

, the angle between two forces is

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

When will a body of mass

20 kg

moving at

15 m s^{- 1},

subjected to a retarding force of

100 N

, come to rest?

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A ball of mass

0.45 kg

which is initially at rest is hit by a bat. The bat remains in contact with the ball for

3 \times 10^{- 3} s

. During this time period the force on the ball by the bat is given as

F (t) = [(α \times 10^{6}) t - (β \times 10^{9}) t^{2}] N

where

α

and

β

are constants. The ball's speed immediately as it loses contact with the bat is

20 m s^{- 1}

. The correct relation between

α

and

β

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A man throws a ball of mass

3.0 kg

with speed of

5.0 m s^{- 1}

. His hand is in contact with the ball for

0.2 s

. If he throws

4

balls in

2

seconds, the average force exerted by him in

1

second is

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. Dependence of force on time is $F \propto t^{n}$ . Initially body is at rest.

Question Image
If the speed of the object is $2 m / s$ at $3 s$ , then the speed at $4 s$ will be approximately (in $m / s$ )

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A particle moving in the

xy

-plane experiences a velocity dependent force

\vec{F} = k (υ_{y} \hat{i} + υ_{x} \hat{j})

, where

υ_{x}

and

υ_{y}

are the

x

and

y

components of its velocity

\vec{υ}

. If

\vec{a}

is the acceleration of the particle, then which of the following statements is true for the particle ?

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

Pick out the correct statement

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A stream of water flowing horizontally with a speed of

15 m s^{- 1}

gushes out of a tube of cross-sectional area

10^{- 2} m^{2}

and hits a vertical wall nearby. The force exerted on the wall by the impact of water (assuming it does not rebound) is

Two masses M1 and M2 are arranged as shown in the figure. Let 'a' be the magnitude of the acceleration of the mass M1. If the mass of M1 is doubled and that of M2 is halved, then the acceleration of the system is (Treat all surfaces as smooth : masses of pulley and rope are negligible )

Important Questions on Laws of Motion

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