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This mock test of Central Forces NAT Level – 2 for IIT JAM helps you for every IIT JAM entrance exam.
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*Answer can only contain numeric values

QUESTION: 1

A man can jump vertically to a height of 1.5*m* on the earth. Calculate the radius of a planet (in *kms* ) of the same mean density as that of the earth from whose gravitational field he could escape by jumping. Radius of earth is 6.41 × 10^{6}*m.*

Solution:

For the asked planet this *u* should be equal to the escape velocity from its surface.

The correct answer is: 3.1

*Answer can only contain numeric values

QUESTION: 2

A particle is projected from point A that is at a distance 4R from the centre of the Earth will speed v_{1} in a direction making joining the centre of the Earth and point A as shown.find the speed v_{2}^{ }if particle passes grazing the surface of the earth Constant interaction only between these two Express you answer in the form (500 × √2X)m/s and write the value of X?

Solution:

let v_{2} to be speed when it grazes earth

Conserving angular momentum we get

mv_{1}sin30^{o}4R = m.v_{2}R.....(i)

Conserving total energy we get

1/2mV_{1}^{2} − GmM/4R

= 1/2 mV_{2}^{2 }− GmM/R

putting V_{2 }= V_{1}sin30^{o }× 4

= 2V_{1} we get

1/2mV_{1}^{2}(1−4) = −3GmM/4R

or

V_{1} =(√Gm/2R)

= (√6.4*10^{7})/2

= 500X√2

X = (8000)/(500*2)

X = 8

*Answer can only contain numeric values

QUESTION: 3

A cord of length 64*m* is used to connect a 100*kg* astronaut. Estimate the value of the tension (in *Newton*) in the cord. Assume that the spaceship is orbiting near earth surface. Also assume that the spaceship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400*km*.

Solution:

As according to given problem the mass of satellite * M* is much greater than that of astronaut

And the equation motion of the astronaut will be

So substituting the given data,

The correct answer is: 0.03

*Answer can only contain numeric values

QUESTION: 4

Ravi can throw a ball a speed on earth which can cross a river of width 10*m*. Ravi reaches on an imaginary planet whose mean density is twice of the earth. If maximum radius of planet so that if Ravi throws the ball at same speed it may escape from planet is **x***km*. then * x* is.

(Given radius of earth = 6.4 × 10^{6}*m*.)

Solution:

Speed of the ball which can cross 10 *m* wide river is

Let the radius of planet is * R*,

Then, mass of planet

Escape velocity of planet

The correct answer is: 4

*Answer can only contain numeric values

QUESTION: 5

An earth satellite is revolving in a circular orbit of radius * a* with velocity

Solution:

Orbital speed of satellite is

From conservation of angular momentum at *P* and *Q*,

From conservation of mechanical energy at *P* and *Q*, we have

Substituting values of *v* and *v*_{0} from Eqs. (i) and (ii), we get

Hence, the maximum and minimum distance are **2 a** and

The correct answer is: 2

*Answer can only contain numeric values

QUESTION: 6

A body is projected vertically upwards from the surface of earth with a velocity sufficient to carry it to infinity. The time taken by it to reach height * h* is given by Find the value of

Solution:

If at a distance *r* from the centre of the earth the body has velocity *v*, by conservation of mechanical energy,

The correct answer is: 1.5

*Answer can only contain numeric values

QUESTION: 7

A projectile of mass * m* is fired from the surface of the earth at an angle α = 60° from the vertical. The initial speed

Solution:

Let * v* be the speed of the projectile at highest point and

Solving these two equation with the given data we get,

or the maximum height

The correct answer is: 0.5

*Answer can only contain numeric values

QUESTION: 8

If a planet was suddenly stopped in its orbit supposed to be circular, it will fall onto the sun in a time times the period of the planet’s revolution. Find the value of * n*.

Solution:

Consider and imaginary planet moving along a strongly extended flat ellipse, the extreme points of which are located on the planet’s orbit and at the centre of the sun. The semi-major axis of the orbit of such a planet would apparently be half the semi-major axis of the planet’s orbit. So the time period of the imaginary planet ** T'** according to Kepler’s law will be given by

∴ Time taken by the planet to fall onto the sun is

The correct answer is: 8

*Answer can only contain numeric values

QUESTION: 9

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the surface of earth. (Radius of the earth = 6400*km* ). If the satellite is stopped suddenly in its orbit and allowed to fall freely on the earth, find the speed (in *m/s*) with which it hits the surface of earth.

Solution:

or h - r - R = R or height = radius of earth.

Increase in kinetic energy = decrease in potential energy

Substituting the values we have,

The correct answer is: 7924

*Answer can only contain numeric values

QUESTION: 10

Two planets of equal mass orbit a much more massive star (figure). Planet **m**_{1 }moves in a circular orbit of radius 1 × 10^{8}*km* with period 2*year*. Planet ** m_{2}** moves in an elliptical orbit with closed distance

Using the fact that the mean radius of an elliptical orbit is the length of the semi-major axis, find the period of m_{2}'s orbit.

Solution:

Mean radius of planet,

The correct answer is: 3.31

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