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

Earn 100

State Aristotle law of motion.

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 :

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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:

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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]

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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

HARD

Physics>Mechanics>Laws of Motion>Force

A helicopter rises from rest on the ground vertically upwards with a constant acceleration

g

. A food packet is dropped from the helicopter when it is at a height

h

. The time taken by the packet to reach the ground is close to [

g

is the acceleration due to gravity]:

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:

HARD

Physics>Mechanics>Laws of Motion>Force

Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_{A}$ and $t_{B}$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$ vertically above $X$ and reaches $X$ in time $t_{C}$ . Choose the correct statement.

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EASY

Physics>Mechanics>Laws of Motion>Force

The given graph shows the variation of velocity $(v)$ with position $(x)$ for a particle moving along a straight line

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Which of the following graph shows the variation of acceleration $(a)$ with position $(x) ?$

State Aristotle law of motion.

Important Questions on Laws of Motion

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