Question 71: Gravitation

Question

$$ 	ext { Match the LIST-I with LIST-II } $$

List - I
List - II

A.
$$	ext { Gravitational constant }$$
I.
$$\left[\mathrm{LT}^{-2}ight]$$

B.
$$	ext { Gravitational potential energy }$$
II.
$$\left[\mathrm{L}^2 \mathrm{~T}^{-2}ight]$$

C.
$$	ext { Gravitational potential }$$
III.
$$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}ight]$$

D.
$$	ext { Acceleration due to gravity }$$
IV.
$$\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}ight]$$

Choose the correct answer from the options given below:

Accepted Answer

HereÃ¢ÂÂs how each quantity lines up with its dimensional formula:
Gravitational constant, $$G$$
Ã¢ÂÂ¢ From NewtonÃ¢ÂÂs law $$F = G\frac{m_1m_2}{r^2}$$
Ã¢ÂÂ¢ $$[G] = \frac{[F]\,[r]^2}{[m]^2} = \frac{(MLT^{-2})\;L^2}{M^2} = M^{-1}L^3T^{-2}$$
Ã¢ÂÂ IV
Gravitational potential energy, $$U$$
Ã¢ÂÂ¢ As work or $$U = mgh$$
Ã¢ÂÂ¢ $$[U] = [F]\,[h] = (MLT^{-2})\;L = ML^2T^{-2}$$
Ã¢ÂÂ III
Gravitational potential, $$\phi$$
Ã¢ÂÂ¢ Energy per unit mass: $$\phi = \frac{U}{m}$$
Ã¢ÂÂ¢ $$[\phi] = \frac{ML^2T^{-2}}{M} = L^2T^{-2}$$
Ã¢ÂÂ II
Acceleration due to gravity, $$g$$
Ã¢ÂÂ¢ Just an acceleration
Ã¢ÂÂ¢ $$[g] = LT^{-2}$$
Ã¢ÂÂ I
Matching them gives
AÃ¢ÂÂIV,Ã¢ÂÂBÃ¢ÂÂIII,Ã¢ÂÂCÃ¢ÂÂII,Ã¢ÂÂDÃ¢ÂÂI
That corresponds to
Option A
.

Answer

A-IV, B-III, C-II, D-I

Answer

A-II, B-IV, C-III, D-I

Answer

A-I, B-III, C-IV, D-II

Answer

A-III, B-II, C-I, D-IV

Gravitation

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