A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential U x = x 4 4 - x 2 2 J , where x is in meters. At time t = 0 s , it is at x = - 0 . 5 m . Then at a later time it can be found,

between x = - 1 . 0 m to x = 0 . 0 m

between x = - 1 . 0 m to x = 1 . 0 m

between x = 0 . 0 m to x = 1 . 0 m

EASY

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Area under velocity-time curve over a given interval of time represents?

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Important Questions on Physics

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Two satellites

S_{1}

and

S_{2}

are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time

t = 0,

the satellites are farthest apart. The periods of revolution of

S_{1}

and

S_{2}

are

3 h

and

24 h

respectively. The radius of the orbit of

S_{1}

3 \times 10^{4} km .

Then the orbital speed of

S_{2}

as observed from

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A very long (length $L$ ) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R < < L)$ . A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$ , then

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Four particles, each of mass

M

and equidistant from each other, move along a circle of radius

R

under the action of their mutual gravitational attraction. The speed of each particle is

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Starting from the center of the earth having radius,

R

, the variation of

g

(acceleration due to gravity) is shown by

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A straight rod of length

L

extends from

x = a

x = L + a .

The gravitational force it exerts on a point mass 'm' at

x = 0,

if the mass per unit length of the rod is

A + B x^{2},

is given by:

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Suppose that the angular velocity of rotation of the Earth is increased. Then, as a consequence,

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A particle is moving in a circle of radius

r

under the action of a force

F = α r^{2}

which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy

= 0

for

r = 0

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A Wheel of moment of inertia

2 k g m^{2}

is rotating about an axis passing through centre and perpendicular to its plane at a speed

60 rad s^{- 1}

. Due to friction, it comes to rest in

5 \min

. The angular momentum of the wheel three minutes before it stops rotating is

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

An automobile moves on a road with a speed of

54 k m h^{- 1}

. The radius of its wheels is

0.45 m

and the moment of inertia of the wheel about its axis of rotation is

3 k g m^{2}

. If the vehicle is brought to rest in

15 s

, the magnitude of average torque transmitted by its brakes to the wheel is:

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Two stones of masses $m$ and $2 m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$ . The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is,

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential

U (x) = \frac{x^{4}}{4} - \frac{x^{2}}{2} J

, where

x

is in meters. At time

t = 0 s

, it is at

x = - 0.5 m

. Then at a later time it can be found,

HARD

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

Take the mean distance of the moon and the sun from the earth to be

0.4 \times 10^{6} km

and

150 \times 10^{6} km

, respectively. Their masses are

8 \times 10^{22}

kg

and

2 \times 10^{30}

kg

, respectively. The radius of the earth is

6400 km

. Let

Δ F_{1}

be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and

Δ F_{2}

be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to

\frac{Δ F_{1}}{Δ F_{2}}

is,

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

The variation of acceleration due to gravity

g

with distance

d

from the centre of the earth is best represented by (

R

= Earth's radius):

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A star mass $M$ (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the centre of mass of star-planet system is shown below:

Question Image

The radius of the planet's orbit is closest to ( $1 AU = Distance Earth and Sun$ )

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

The depth

d

at which the value of acceleration due to gravity becomes

\frac{1}{n}

times the value at the earth's surface is

(R

= radius of the earth

)

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

A ball is launched from the top of Mount Everest which is at an elevation of

9000 m

. The ball moves in a circular orbit around the earth. The acceleration due to gravity near the earth's surface is

g

. The magnitude of the ball's acceleration while in orbit is,

MEDIUM

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

The International space station is maintained in a nearly circular orbit with a mean altitude of

330 km

and a maximum of

410 km

. An astronaut is floating in the space station's cabin. The acceleration of astronauts as measured from the earth is-

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

If the change in the value of

g

at a height

h

above the surface of the earth is the same as at a depth

x

below it, then (both

x

and

h

being much smaller than the radius of the earth)

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

At what height from the surface of earth the gravitation potential and the value of g are

- 5.4 \times 10^{7} J k g^{- 2}

and

6.0 m s^{- 2}

respectively? Take the radius of earth as

6400 km

EASY

Reasoning and General Awareness>General Knowledge and Current Affairs>Physics>Mechanics

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

Area under velocity-time curve over a given interval of time represents?

Important Questions on Physics

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