Question

There is an old physics joke involving cows, and you will need to use its punchline to solve this problem
A cow is standing in the middle of an open, flat field. A plumb bob with a mass of 1 kg is suspended via an unstretchable string 10 meters long so that it is hanging down roughly 2 meters away from the center of mass of the cow. Making any reasonable assumptions you like or need to, estimate the angle of deflection of the plumb bob from vertical due to the gravitational field of the cow.

Answer 1

Answer:

The angle of deflection will be "1.07 × 10⁻⁷°".

Explanation:

The given values are:

Mass of a cow,

m = 1100 kg

Mass of bob,

mb = 1 kg

The total distance between a cow and bob will be,

d = 2 m

Let,

The tension be "t".

The angle with the verticles be "$\theta$".

Now,

Vertically equating forces

⇒  $T\times Cos \theta =mb\times g$ ...(equation 1)

Horizontally equating forces

⇒  $T\times Sin \theta = G\times M\times \frac{mb}{d^2}$ ...(equation 2)

From equation 1 and equation 2, we get

⇒  $tan \thata=\frac{G\times M}{g\times d^2}$

O putting the estimated values, will be

⇒  $\theta = tan(\frac{6.674\times 10^{-11}\times 1100}{9.8\times 2^2} )$

⇒  $\theta = 1.07\times 10^{-7}^{\circ}$