APRIL, 24
1. Which of the following is the evidence to show that there must be a force acting on earth
and directed towards the sun
(a) Deviation of the falling bodies towards east
(b) Revolution of the earth round the sun
(c) Phenomenon of day and night
(d) Apparent motion of sun round the earth
2. If the distance between two masses is doubled, the gravitational attraction between them
(a) Is doubled (b) Becomes four times
(c) Is reduced to half (d) Is reduced to a quarter
3. Which of the following statements about the gravitational constant is true
(a) It is a force
(b) It has no unit
(c) It has same value in all systems of units
(d) It depends on the value of the masses
(e) It does not depend on the nature of the medium in which the
bodies are kept.
4. If the earth rotates faster than its present speed, the weight of an object will
(a) Increase at the equator but remain unchanged at the poles
(b) Decrease at the equator but remain unchanged at the poles
(c) Remain unchanged at the equator but decrease at the poles
(d) Remain unchanged at the equator but increase at the poles
5. If the earth suddenly shrinks (without changing mass) to half of its present radius, the
acceleration due to gravity will be
(a) g/2 (b) 4g (c) g/4 (d) 2g
SECTION B
6. An 80.0-kg passenger in an SUV traveling at 1.00 10 2 km/h is wearing a seat belt. The
driver slams on the brakes and the SUV stops in 45.0 m. Find the force of the seat belt on
the passenger.
Solution
v2 (27.8 m/s)2
v 2 = v02 + 2ax a 0 = = 8.59 m/s 2
2x 2(45.0 m)
Fnet ma (80.0 kg)(8.59 m/s2 ) 687 N
7. The weight of an astronaut plus his space suit on the Moon is only 250 N. (a)
How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon?
On Earth?
Solution
wMoon mg Moon
wMoon 250 N
m 150 kg ;
g Moon 1.67 m/s 2
wEarth mg Earth 150 kg 9.8 m/s 2 1470 N 1.5 103 N
8. Mass of sun: 1.99 × 1030 kg, Radius of Sun 1.496 × 1011 m and the Radius of earth 6.38
×106 m
a. Find the gravitational force exerted by the Sun on a 70.0-kg man located at the
Earth’s equator at noon, when the man is closest to the Sun? [2]
Answer: F = GmM/(r-Re)2 0.415N
b. Calculate the gravitational force of the Sun on the man at midnight, when he is
farthest from the Sun. ? [2]
F = GmM/(r+Re)2 Answer: 0.415 N
c. Calculate the difference in the acceleration due to the Sun between noon and
midnight. ∆F= ma 1.0 ×10-6 m/s2 ? [2]
9. A 0.046 kg golf ball hit by a driver can accelerate from rest to 67 m/s in 1 ms while the
driver is in contact with the ball. How much average force does the golf ball experience
?? [2]
𝒗=𝒂𝒕+𝒗_𝟎
𝟔𝟕 𝒎/𝒔=𝒂(𝟏×𝟏𝟎^(−𝟑) 𝒔)+𝟎
𝟔𝟕𝟎𝟎𝟎 𝒎/𝒔^𝟐 =𝒂
𝑭=𝒎𝒂
𝑭=(𝟎.𝟎𝟒𝟔 𝒌𝒈)(𝟔𝟕𝟎𝟎𝟎 𝒎/𝒔^𝟐 )
𝑭=𝟑𝟎𝟖𝟐 𝑵
10. Calculate the weight of a person of mass 75 kg if they are on the moon where the gravitational
field strength is 1.6 N kg-1. ? [2]
Weight = 75 x 1.6 (1M)
= 120 N (1A)
11. Derive the equation which relates the time period of orbit and its distance away from the
centre of the Earth which leads to Kepler’s 3rd law:
? [5]
G M m / r2 = m v2 / r (1M) or m ω2 r
G M / r = v2
v2 = 4 π2 r2 / T2
T2 = 4 π2 r3 / (G M) (1M)
12. A geostationary satellite orbits the Earth above the equator with a period of 24 hours.
If the mass of the Earth is 6.0 x 1024 kg and the radius of the Earth is 6400 km, determine the
height of the satellite above the Earth’s surface. ? [3]
T2 G M / 4 π2 = r3
T = 24 x 60 x 60
= 86 400 s
R3 = 86 4002 x 6.67 x 10-11 x 6.0 x 1024 / 4 π2 (1M)
R = 42.3 x 106 m (1A)
Height above earth = 42.3 x 106 – 6400 x 103 (1A)
= 35.9 x 106 m (1A)
