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

EASY

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All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2 kg$ is :

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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 ?

MEDIUM

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

Two blocks of masses

m_{1}

and

m_{2}

are suspended by a massless string passing over a smooth pulley. If the acceleration of the system is

\frac{g}{8},

then the ratio of the masses

\frac{m_{2}}{m_{1}} =

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 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.

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 block of mass

48 kg

kept on a smooth horizontal surface is pulled by a rope of length

4 m

by a horizontal force of

25 N

applied to the other end. If the linear density of the rope is

0.5 kg m^{- 1},

the force acting on the block is

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

Two bodies of mass

4 kg

and

6 kg

are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity

(g)

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,

HARD

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

The machine as shown has $2$ rods of length $1 m$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a $2 kg$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

Question Image

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

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

Two blocks $A$ and $B$ of masses $1.5 kg$ and $0.5 kg$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block A is lifted until block B touches the ground and then block A is released. The initial height of block A is $80 cm$ when block B just touches the ground. The maximum height reached by block $B$ from the ground after the block A falls on the ground is

Question Image

MEDIUM

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

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05 .$ ( $g = 10 m s^{- 2},$ mass of the string is negligible and no other friction exists).

Question Image

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

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

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

Important Questions on Laws of Motion

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All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2 kg$ is :