Question

 

Q11. A heavy mass and a lighter mass are dropped from the same height. Let be the acceleration due to gravity. Pick the correct alternative from the following statements.(Assume there is no air friction present)



A) for mass will be higher than that of B) for mass will be lower than that of

mass mass

C) for both the masses will be same but will D) for both the masses will be same and reach the ground earlier both will reach the ground at the same time​

Answer 1

Answer:

Explanation:

(a) Acceleration decreases according to formula g  

′

=g(1−  

R

2h

​

),

where h is height and R is radius of earth.

(b) Acceleration decreases according to formula g  

′

=g(1−  

R

d

​

),

where d is depth and R is radius of earth.

(c) Acceleration due to gravity is given by the formula: g=  

R  

e

2

​

 

GM  

e

​

 

​

 

Hence, it is independent of mass of body, but is dependent on mass of earth.

(d) Gravitational potential energy is given by the formula: U=−  

r

Gm  

1

​

m  

2

​

 

​

 

g=  

R  

e

2

​

 

GM  

e

​

​

 assuming distance between object and earth is nearly equal to the radius of the earth.

Substituting the second equation in first, we get U≈mgh

Hence, the first formula is more accurate.

Answer 2

The correct alternative is:

g for both the masses will be the same and both will reach the ground at the same time​. (option D)

What is the acceleration due to gravity?

• Acceleration due to gravity is the acceleration of a body falling freely under the influence of the Earth's gravitational pull.
• It is the same for all objects. It is denoted as 'g'.
• It is roughly equal to 9.8 m/s².

Formula For g

• Let us assume a body of mass 'm' kg experiences a gravitational force F from the Earth.
• Let the mass of the Earth be M kg and the distance between the object and Earth be r m.
• Then F is given by:

                                        F = $\frac{GMm}{r^{2} }$                                  (1)

where G is the universal Gravitational constant (= 6.67 × $10^{-11}$)

• From Newton's Laws, we also know that:

                                Force = mass × acceleration

Here, the mass of the object is m

and acceleration due to gravity is g.

                                  ⇒ F =mg

• Substituting this value of F in (1):

                                 ⇒ mg = $\frac{GMm}{r^{2} }$

                                 ⇒ g = $\frac{GM}{r^{2} }$

Thus it is clear that g does not depend on the mass of the object.

Hence both lighter and heavier mass will experience g equally and thus, reach the ground at the same time.

So option D is correct.