Question

Three spheres have radii 1 cm, 2 cm and 3 cm respectively. Which sphere
exerts maximum pressure on earth if masses of all three are same?
(a) First (r = 1 cm)
(b) Second (r= 2 cm)
(c) Third (r = 3 cm)
(d) All equal​

Answer 1

Refer to the attachment

Answer 2

Given :

Three spheres having radii :

1 cm , 2 cm and 3 cm for 1st , 2nd and 3rd sphere respectively.

Masses of all the three spheres are same .

To Find :

Which sphere exerts maximum pressure on earth ?

Solution :

Ideally there is only on point of contact between a sphere and a plane and no surface area .

But actually the sphere get distorted due to their own weight and since it is given that the mass of all the spheres  are equal , so extent of distortion will be equal .

Now , surface area of 1st sphere  $= 4\pi (1)^{2} = 4\pi$

Surface area of 2nd sphere $= 4\pi(2)^{2}= 16\pi$

Surface area of 3rd sphere $= 4\pi(3)^{2} = 36\pi$

We know that formula for pressure P is :

$P=\frac{Force }{Area}$  

So pressure is inversely proportional to area .

So the pressure exerted by 1st sphere is maximum because its surface area is minimum.

So the correct ans is (A) 1st sphere