Gravitational Constant: Overview, Questions, Preparation

Every body in the universe attracts every other body with force directly proportional to their masses' product and inversely proportional to the square of the distance between them.

F = Gravitational force

m1, m2 = masses of the bodies

r = distance between two masses

G = Universal Gravitational Constant

The value of the gravitational constant in SI units is 6.674×10−11 m3⋅kg−1⋅s−2 . The gravitational constant G value was experimentally determined in 1798 by Henry Cavendish.

Cavendish Experiment

• The small lead spheres attached to the rods' end are suspended on a fine wire with support. 
• When the rod gets twisted, the wire's torsion exerts a torsional force proportional to the angle of rotation of the rod.
• When 2 bigger lead spheres are kept near the small spheres attached to the rod, the bigger spheres exert a gravitational force upon smaller spheres. 
• The suspending wire gets contorted till the restoring torque gets equal to the gravitational torque.
• If θ is the angle of contortion of the suspending wire, the restoring torque is proportional to θ, equal to τθ. τ is the restoring couple per unit angle of twist. 
• By this experiment, Cavendish was able to determine the gravitational pull of attraction between two masses.

• If the length of the bar AB is L, then the torque arising from F is Fx At equilibrium, it equals the restoring torque and hence:

• From the above equation, the observation of θ enables us to calculate the G. From the Cavendish experiment, G has the value of 6.674×10−11 Nm²/kg².

Gravitational constant for Class 11

The gravitational constant is used to show the force exerted between Newton's two objects through his gravitation law. Through this topic, one knows about the G and its value derived by the Cavendish through his experiments. The weightage of the topic is around 5%.

Example 1: If the body of mass is 40 kg is attracted by another mass of 15 kg by a force of 9.8x10⁻⁷ N and the distance between the masses is 0.2m, find G.

G = Fd²/Mm

G = 9.8x10⁻⁷x 0.2²/ 40x15 

G = 6.533 x 10⁻¹¹ Nm²/kg²

Example 2: Calculate the gravitational constant if the mass of the planet and earth is equal to 5.98 x 10²⁴ kg, where the distance of the planet from the earth is 2.5 x 10⁷km and the gravitational force exerted by them is 3.82 x 10¹⁸ N.

G = 3.82 x 10¹⁸(2.5 x 10⁷)²/5.98 x 10²⁴ (5.98 x 10²⁴ )

G = 6.67×10−11 Nm²/kg²

Example 3: What is the gravitational force between two atoms separated by a distance of 1 angstrom. Mass of the atom is 1.6×10⁻²⁷ kg.

Distance r = 1A = 10⁻¹⁰m

F = 6.67× 10⁻¹¹( 1.6×10⁻²⁷) 1.6×10⁻²⁷/(10⁻¹⁰)²

F = 17× 10⁻⁴⁵ N

Images courtesy: NCERT