Gravitation Test

Result

Gravitation Test - 81

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Weekly Quiz Competition

Question 1
1 / -0

A particle hanging from a massless spring stretch it by $$2 cm$$ at earths surface. How much will the same particle stretch the spring at height $$2624 km$$ from the surface of earth $$?$$ (radius of earth 6400 km)

A
$$1 cm$$

B
$$2 cm$$

C
$$3 cm$$

D
$$4 cm$$
Question 2
1 / -0

The magnitude of gravitational potential at a distance $$\frac {a}{2}$$ from the center

A
$$\dfrac { - 15GM } { 4 a }$$

B
$$\dfrac { - 4GM } { 9 a }$$

C
$$\dfrac { -11GM } { 8 a }$$

D
$$\dfrac { - 6GM } { 7 a }$$

Solution
Question 3
1 / -0

A body of mass 2 kg is thrown into space with escape velocity 11.2 km/s, the escape velocity for another body of mass 5 kg will be

A
38 km/s

B
22.4 km/s

C
50.6 km/s

D
11.2 km/s

Solution
Question 4
1 / -0

At what height $$h$$ above the earth surface, the value of $$g$$ becomes $$\dfrac{g}{2}$$? (where $$R$$ is the radius of the earth)

A
$$(\sqrt 2 - 1)R$$

B
$$\sqrt 2 R$$

C
$$(\sqrt 2 + 1)R$$

D
$$R\sqrt 2$$

Solution
Question 5
1 / -0

A man in a balloon rising vertically with an acceleration of $$4.9m/sec^2$$ releases a ball $$2$$ sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is $$(g=9.8m/sec^2)$$

A
$$14.7m$$

B
$$19.6m$$

C
$$9.8m$$

D
$$24.5m$$

Solution

$$a=4.9㎨$$
Initial velocity $$=0$$
Velocity of balloon and ball after $$2$$ sec
$$v=u+at=9.8㎧$$
Height at this point
$$h=\cfrac { 1 }{ 2 } a{ t }^{ 2 }$$
$$=0.5\times 4.9\times 4$$
$$=9.8m$$
The ball will attain further height $$=s$$
$$\cfrac { 1 }{ 2 } m{ v }^{ 2 }=mgs$$
$$s=\cfrac { { v }^{ 2 } }{ 2g } =4.9m$$
Greatest height that can be achieved
$$H=h+s=9.8+4.9=14.7m$$
Question 6
1 / -0

The height at which the acceleration due to gravity becomes $$g/9$$ (where $$g=$$ the acceleration due to gravity on the surface of the earth) in terms of $$R$$, (the radius of the earth) is:-

A
$$\frac {R}{2}$$

B
$$\sqrt 2 R$$

C
$$2R$$

D
$$\frac {R}{\sqrt 2}$$

Solution
Question 7
1 / -0

If retardation produced by air resistance of air resistance is one - tenth of acceleration due to gravity. the time to reach maximum height.

A
Decrease by 11 percent

B
Increase by 11 percent

C
Decrease by 9 percent

D
Increase by 9 percent

Solution
Question 8
1 / -0

A body weighs W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be:

A
$$\dfrac { W }{ 2 } $$

B
$$\dfrac { 2W }{ 3} $$

C
$$\frac {4 W }{ 9 } $$

D
$$\frac { W }{ 4 } $$

Solution
Question 9
1 / -0

A body weighted 980 N on the surface of the earth. It weight half way down to the centre of the earth is (Assume earth to be of uniform density)

A
490 N

B
125 N

C
1960 N

D
Zero

Solution
Question 10
1 / -0

A man weights 100 kgf on the surface of earth. At what height above the surface of earth his weight will be 50 kgf? [where R is radius of the earth]

A
$$\frac{R}{4}$$

B
$$\frac{R}{2}$$

C
$$(\sqrt3 - 1)R$$

D
$$(\sqrt2 - 1)R$$

Solution