Phys101
Term:122
Online HW-Ch13-Lec02
Q1:
A spherical shell has inner radius R 1 , outer radius R 2 , and mass M,
distributed uniformly throughout the shell. The magnitude of the
gravitational force exerted on the shell by a point mass m, located a
distance d from the center, outside the outer radius, is:
A.
B.
C.
D.
E.
Ans:
C; |F| =
M
0
G Mm/R 1 2
G Mm/d2
G Mm/(R 2 2-d2)
G Mm/(R 1 2-d2)
m
d
R1
𝐑𝟐
GMm
GMm
=
r2
d2
Q2:
Three equal masses, 2.0 kg each, are placed at the three corners of a square of side a =
10 cm as shown in the figure. Find the magnitude of the gravitational potential energy
(in J) of the system of three particles. (Give your answer in three significant figures
form)
2
1
𝑎√2
3
Ans:
r12 = r13 = a = 0.1 m
r23 = a√2 = 0.1 × √2 = 0.1 × √2 = 0.14 m
|U| = |U12 + U13 + U23 | = �−
= +6.67 × 10−11 × 2 × 2 �
KFUPM-Physics Department
Gm1 m2 Gm1 m3 Gm2 m3
−
−
�
r12
r13
r23
1
1
1
+
+
� = +7.23 × 10−9 J
0.1 0.1 0.14
1
Phys101
Term:122
Online HW-Ch13-Lec02
Q3:
The escape speed at the surface of Earth is approximately 8×103 m/s.
If we have a planet whose radius R = 2R E , and has an escape speed
twice that for Earth, find the mass (in kg) of the planet. Given the
radius and mass of Earth as R E = 6.370×106 m and M E = 5.98×1024
kg, respectively. (Give your answer in three significant figures form)
𝐀𝐧𝐬:
There are many methods for solving this question, one of them is:
vplanet = 2vEarth ; where vescape = �
2GMp
�
Rp
2GME
= 2�
RE
; given R p = 2R E
Square both sides ⇒
2GM
R
(2GME )
2GMP
=4
(2R E )
RE
⇒ MP = 8ME = 8 × 5.98 × 1024 = 4.78 × 1025 kg
KFUPM-Physics Department
2