Gravitation

MCQs (Part - VI)

Question 26: A sphere of mass M and radius R2 has a concentric cavity of ratius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located a distance r from the centre of sphere varies as :

Answer: (b)

Explantion: The whole space can be divided into three regions

(i) 0 < r < R1, F(r) = 0

(ii) Rl < r < R2, F(r)

(iii) R2 < r < , F(r)

Here, r is the density of material of the sphere.

Question 27: If the radius of earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?

  1. Decreases by 19%
  2. Increases by 19%
  3. Decreases by more than 19%
  4. Increases by more than 19%

Answer: (d) Increases by more than 19%

Question 28: A man covers 60 m distance in one minute on the surface of earth. the distance he will cover on the surface of moon per mumute is : (Assuming gmoon )

  1. 60 m
  2. 60 × 6 m
  3. m
  4. m

Answer: (a) 60 m

Explantion: In a linear motion on plane surface there is no effect of gravity on motion of man on moon's surface.

Question 29: A body is suspended on a spring balance in a ship sailling along the equator with a speed v'. If w is the angular sppeed of the earth and w0 is the scale reading when the ship is at rest, the scale reading when the ship is sailling, will be very close to:

  1. w0
  2. none of these

Answer: (c)

Question 30: If earth were to rotate faster than its persent speed, the weight of an object will:

  1. increase at the equator but remain unchanged at poles
  2. decrease at the equator but remain unchanged at the poles.
  3. remain unchanged at the equator but decrease at the poles
  4. remain unchanged at the equator but increase at the ploes

Answer: (b) decrease at the equator but remain unchanged at the poles.

Explanation The value of acceleration due to gravity at latitude l is

g' = g - Rw2 cos2 l

At equator l = 0, so

g'e = g - Rw2 ...(i)

At poles l = 90, so

g'p = g ...(ii)

If earth rotates faster then from Eq. (i),

g'e < g


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