Examples on Universal Gravitational Constant
Example 1: Two particles of equal mass “m” go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their center of mass is
- (A) √Gm/R
- (B) √Gm/4R
- (C) √Gm/3R
- (D) √Gm/2R
Solution:
Option (B) is Correct
Gm2/4R2 = mV2/R
V = √Gm/4R
Example 2: A simple pendulum has a time period T1 when on the earth’s surface, and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T2/T1 is
- (a) 1
- (b) 3
- (c) 4
- (d) 2
Solution:
Option (d) is Correct
Time period of a simple pendulum = 2π√l/g
On the surface of earth g1 = GM/R2
At a height R above the earth g2 = GM/(2R)2(g1/g2) = (4/1)T = 2π√(l/g)
Time period on the surface of the earth T1 = 2π√l(R)2/GM
Time period on the surface of the earth T2 = 2π√l(2R)2/GMT2/T1 = 2
Example 3: The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km respectively. The required energy for this work will be
- (a) 6.4 x 1010 Joules
- (b) 6.4 x 1011 Joules
- (c) 6.4 x 108 Joules
- (d) 6.4 x 109 Joules
Solution:
Option (a) is Correct
Energy required is given by = GMm/R
= gR2 ×m/R (∵g = GM/R2)
= mgR = 1000 × 10 × 6400 × 103= 64 × 109 J= 6.4 × 1010 J
Universal Gravitational Constant
Universal Gravitational Constant Value is,
G = 6. 6743 x 10-11 N.m2.kg -2 or 6.6743×10-8 Dyn.cm2.g-2
Universal Gravitational Constant is a physical constant involved in the calculations of gravitational effects. It is the gravitational force acting between two bodies of unit mass. The Universal Gravitational Constant is used in different formulas of Gravitation.
In this article, we will look into the Universal Gravitational Constant, Universal Gravitational Constant Dimension, Universal gravitational constant Value, and others in detail.
Table of Content
- What is a Universal Gravitational Constant?
- Newton’s Universal Gravitation Law
- Universal Gravitational Constant Mathematical Representation
- Application of Universal Gravitational Constant
- Examples on Universal Gravitational Constant