A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as d K d t = γ t , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

The distance of the particle from the origin increases linearly with time

EASY

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State whether the given statement is true or false.

An external force required to keep a body in uniform motion.

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Force

Two blocks

A

and

B

of masses

3 m

and

m

respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of

A

and

B

immediately after the string is cut, are respectively
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EASY

Physics>Mechanics>Laws of Motion>Force

Three blocks A, B and C, of masses

4 kg, 2 kg

1 kg

and respectively, are in contact on a frictionless surface, as shown. If a force of

14 N

is applied on the

4 kg

block, then the contact force between A and B is:

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HARD

Physics>Mechanics>Laws of Motion>Force

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>Force

Two masses

m_{1} = 5 kg

and

m_{2} = 10 kg

, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is

0.15

. The minimum weight

m

that should be put on top of

m_{2}

to stop the motion is:

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Force

A mass of

10 kg

is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of

45 °

at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is

(g = 10 m s^{- 2})

HARD

Physics>Mechanics>Laws of Motion>Force

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
(density of water is

ρ_{w}

)

MEDIUM

Physics>Mechanics>Laws of Motion>Force

An elevator of mass

m

is connected to a rope which pulls the elevator up with a maximum acceleration equal to

a

. If the maximum bearable tension in the rope is

T

, then for a safe journey the minimum diameter of the rope is [

g

= acceleration due to gravity]

HARD

Physics>Mechanics>Laws of Motion>Force

A block of weight

100 N

is suspended by copper and steel wires of same cross-sectional area

0.5 c m^{2}

and, length

\sqrt{3} m

and

1 m,

respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are

30^{o}

and

60^{o},

respectively. If elongation in copper wire is

(Δ l_{C})

and elongation in steel wire is

(Δ l_{S}),

then the ratio

\frac{Δ l_{C}}{Δ l_{S}}

\frac{x}{1}

.Find the value of

x

.
[Young's modulus for copper and steel are

1 \times 10^{11} N m^{- 2}

and

2 \times 10^{11} {Nm}^{- 2}

respectively]

Question Image

HARD

Physics>Mechanics>Laws of Motion>Force

A particle of mass

m

is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as

\frac{d K}{d t} = γ t,

where

γ

is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

MEDIUM

Physics>Mechanics>Laws of Motion>Force

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

HARD

Physics>Mechanics>Laws of Motion>Force

A particle of mass

m

is acted upon by a force

F

given by the empirical law

F = \frac{R}{t^{2}} v (t) .

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

MEDIUM

Physics>Mechanics>Laws of Motion>Force

A vehicle moving at

36 km / h

is to be stopped by applying brakes in the next

5 m .

If the vehicle weight

2000 kg,

determine the average force that must be applied on it

MEDIUM

Physics>Mechanics>Laws of Motion>Force

A block of mass

10 k g

is in contact against the inner wall of a hollow cylindrical drum of radius

1 m

. The coefficient of friction between the block and the inner wall of the cylinder is

0.1

. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be

(g = 10 m s^{- 2})

EASY

Physics>Mechanics>Laws of Motion>Force

A spring of force constant

k

is cut into lengths of ratio

1 : 2 : 3

. They are connected in series and the new force constant is

k'

. If now they are connected in parallel and force constant is

k''

, then

k' : k''

EASY

Physics>Mechanics>Laws of Motion>Force

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle $P Q R$ . The velocity of the particle will
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MEDIUM

Physics>Mechanics>Laws of Motion>Force

A ball is thrown vertically up (taken as

+ z - a x i s

) from the ground. The correct momentum-height

(p - h)

diagram is:

HARD

Physics>Mechanics>Laws of Motion>Force

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>Force

A rod of weight

W

is supported by two parallel knife edges

A

and

B

and is in equilibrium in a horizontal position. The knives are at a distance

d

from each other. The centre of mass of the rod is at distance

x

from

A

. the normal reaction on

A

is:

MEDIUM

Physics>Mechanics>Laws of Motion>Force

A spherical body of mass $2 kg$ starting from rest acquires a kinetic energy of $10000 J$ at the end of $5^{th}$ second. The force acted on the body is _____ $N$ .

HARD

Physics>Mechanics>Laws of Motion>Force

In an hour-glass approximately 100 grains of sand fall per second (starting from rest); and it takes

2 s

for each sand particle to reach the bottom of the hour-glass. If the average mass of each sand particle is

0.2 g

, then the average force exerted by the falling sand on the bottom of the hour-glass is close to

State whether the given statement is true or false. An external force required to keep a body in uniform motion.

Important Questions on Laws of Motion

Learn and Prepare for any exam you want !

State whether the given statement is true or false.

An external force required to keep a body in uniform motion.