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

The force acting on a particle is given by α β → × p → where α is a constant, β → is a constant vector of magnitude β and p → is the linear momentum of the particle. Then

the magnitude of p → is a constant.

the dimension of α β is M · T - 1 .

HARD

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Two blocks of masses $m$ and $n m$ are connected by a massless string passing over a frictionless pulley. The value of $n$ for which both the blocks moves with an acceleration of $g / 10$ is

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Important Questions on Laws of Motion

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 ?

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 ?

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,

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

Pick out the correct statement

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 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

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

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

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

The pair with same dimension is ___.

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

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,

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 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

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

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 ?

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?

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:

EASY

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

The force acting on a particle is given by

α \vec{β} \times \vec{p}

where

α

is a constant,

\vec{β}

is a constant vector of magnitude

β

and

\vec{p}

is the linear momentum of the particle. Then

Two blocks of masses m and nm are connected by a massless string passing over a frictionless pulley. The value of n for which both the blocks moves with an acceleration of g/10 is

Important Questions on Laws of Motion

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Two blocks of masses $m$ and $n m$ are connected by a massless string passing over a frictionless pulley. The value of $n$ for which both the blocks moves with an acceleration of $g / 10$ is