Gravitation Test

Result

Gravitation Test - 85

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Weekly Quiz Competition

Question 1
1 / -0

A capillary tube is immersed vertically in water and the height of the water column is X. When this arrangement is taken into a mine of depth d, the height of the water column is Y. If R is the radius of the earth, the ratio X/Y is

A
$$1-\dfrac{d}{R}$$

B
$$1$$+$$\dfrac{d}{R}$$

C
$$\dfrac{R-d}{R+d}$$

D
$$\dfrac{R+d}{R-d}$$

Solution
Question 2
1 / -0

The gravitational force in a region is given by
$$\vec{E}=ay\hat i+ax \hat j$$
The work done by gravitational force to shift a point mass $$m$$ from $$(0, 0, 0)$$ to $$(x_0, y_0, z_0)$$ is :

A
$$ma\ x_0y_0z_0$$

B
$$ma\ x_0y_0$$

C
$$-ma\ x_0y_0$$

D
$$zero$$

Solution
Question 3
1 / -0

The gravitational field in a region is $$10\ N/kg (\hat i -\hat j)$$. The work done by external agent to shift slowly a particle of mass $$1\ kg$$ from point $$(1\ m, 1\ m)$$ to a point $$(2\ m, -2\ m)$$ is :

A
$$40\ joule$$

B
$$-40\ joule$$

C
$$zero$$

D
$$+10\ joule$$

Solution
Question 4
1 / -0

A gravitational field is present in a region. A point mass is shifted from $$A$$ to $$B$$, from different paths shown in the figure. If $$W_1, W_2$$ and $$W_3$$ represent work done by gravitational force for respective paths, then :

A
$$W_1=W_2=W_3$$

B
$$W_1>W_2W_3$$

C
$$W_1>W_3>W_2$$

D
none of these

Solution
Question 5
1 / -0

The body of masses $$'m'$$ is raised through a height above the surface of the earth so that the increase in $$P.E.$$ is $$mgR/5$$ where $$'R'$$ is the radius of the earth. The height to which the body is raised is

A
$$R/8$$

B
$$R/5$$

C
$$R/2$$

D
$$R/4$$

Solution
Question 6
1 / -0

If the earth suddenly contracted to half of its radius without any change in its mass and its shape, duration of the day instead of $$24$$ hours will be :

A
$$24$$ hours

B
$$12$$ hours

C
$$6$$ hours

D
$$8$$ hours

Solution
Question 7
1 / -0

The mass of a balloon with its contents is $$1.5\, kg$$. It is descending with an acceleration equal to half that of acceleration due to gravity. If it is to go up with the same acceleration keeping the volume same, its mass should be decreased by :

A
$$1.2\, kg$$

B
$$1\, kg$$

C
$$0.75\, kg$$

D
$$0.5\, kg$$

Solution
Question 8
1 / -0

The acceleration due to gravity at a height $$\cfrac {R}{20}$$ from the surface is $$9m/s^2$$ Its value at a point at an equal distance below the surface of the earth is

A
$$8.563 ms^{-2}$$

B
$$8.832 ms^{-2}$$

C
$$9.426 ms^{-2}$$

D
$$9.242 ms^{-2}$$

Solution
Question 9
1 / -0

The work done by external agent to shift a point mass from infinity to the centre of earth is :

A
$$=0$$

B
$$>0$$

C
$$<0$$

D
$$<0$$

Solution

Work done by external agent is
$$W= m(dV)$$

$$dV=$$ change in potential energy.

So, $$ W= m(V_2- V_1)$$.....(i)

At infinity $$V_1= 0$$

On the center of earth , $$V_2= \dfrac{-3GM}{2R}$$...(ii)

Putting (i) equation in equation (ii) we get,

$$ W= m\dfrac{-3GM}{2R}$$

$$W= \dfrac{-3GMm}{2R}$$

This shows that work done cannot be zero.

Here, Work done is negative

which results in $$W<0$$

Option (C) is correct.
Question 10
1 / -0

Directions For Questions

A block of mass $$M\ kg$$ is dropped onto a verticle spring force constant $$k\ Nm^{-1}$$. The block stick to the spring, and the spring compresses $$x\ m$$ before coming momentarily to rest.

...view full instructions

During the compression of the spring the work done by the force of gravity is

A
$$Mgx$$

B
$$\left(\dfrac {1}{2}\right)kx^2$$

C
$$-\left(\dfrac {1}{2}\right)kx^2$$

D
$$Mgx + \left(\dfrac {1}{2}\right)kx^2$$

Solution