MHT CET · Physics · Gravitation

Consider a particle of mass m suspended by a string at the equator. Let R and M denote radius and mass of the earth. If $ω$ is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be $(c o s 0^{o} = 1)$

A $\frac{G M m}{R^{2}}$
B $\frac{G M m}{2 R^{2}}$
C $\frac{G M m}{2 R^{2}} + m ω^{2} R$
D $\frac{G M m}{R^{2}} - m ω^{2} R$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{G M m}{R^{2}} - m ω^{2} R$

Step-by-step Solution

Detailed explanation

When a body suspended by the string situated at position

P

as shown in the figure, where latitude is

λ

, then body is also rotated with angular frequency

(ω)

of earth, hence tension on the string is given by

T = m g - m ω^{2} c o s λ

T = m . \frac{G M}{R^{2}} - m ω^{2} c o s λ [∴ g = \frac{G M}{R^{2}}]

T = \frac{G M m}{R^{2}} - m r ω^{2} c o s λ

…. (i)
When body is suspended at equator, then

λ = 0

and

r = R

∴

From Eq. (i), we have,

T = \frac{G M m}{R^{2}} - m R ω^{2} c o s 0^{o}

T = \frac{G M m}{R^{2}} - m R ω^{2}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Consider a particle of mass m suspended by a string at the equator. Let R and M denote radius and mass of the earth. If ω is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be cos0o=1

Step-by-step Solution

Consider a particle of mass m suspended by a string at the equator. Let R and M denote radius and mass of the earth. If $ω$ is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be $(c o s 0^{o} = 1)$