Question 52: Gravitation

Question

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$	imes$$ 4 matrix given in the ORS.

Column I

Column II

(A)
GM$$_e$$M$$_s$$G - universal gravitational constant,M$$_e$$ - mass of the earth,M$$_s$$ - mass of the Sun
(P)
(volt)(coulomb)(metre)

(B)
$${{3RT} \over M}$$R - universal gas constant,T - absolute temperature,M - molar mass
(Q)
(kilogram)(metre)$$^3$$(second)$$^{-2}$$

(C)
$${{{F^2}} \over {{q^2}{B^2}}}$$F - force,q - charge,B - magnetic field
(R)
(metre)$$^2$$(second)$$^{-2}$$

(D)
$${{G{M_e}} \over {{R_e}}}$$G - universal gravitational constant,M$$_e$$ - mass of the earthR$$_e$$ - radius of the earth
(S)
(farad)(volt)$$^2$$(kg)$$^{-1}$$

Accepted Answer

Reason : Unit of $$G{M_e}{M_s} = F{r^2} = N{m^2}$$
$$ = kg{m \over {{s^2}}} 	imes {m^2}$$
$$ = Kg{m^3}{s^{ - 2}}$$
Also (volt)(coulomb)(metre) = (Joule)(metre)
= (N $$-$$ m)(m) = Nm$$^2$$ = Kgm$$^3$$s$$^{-2}$$
A $$	o$$ P, Q
Reason : $${v_{rms}} = \sqrt {{{3RT} \over M}} $$
$$ \Rightarrow v_{rms}^2 = {{3RT} \over M}$$
Unit of $${{3RT} \over M}$$ is m$$^2$$s$$^{-2}$$
Also (farad)(volt)$$^2$$(kg)$$^{-1}$$ = (joule)(kg$$^-1$$)
= N-mkg$$^{-1}$$ = kgms$$^{-2}$$mkg$$^{-1}$$ = m$$^2$$s$$^{-2}$$
B $$	o$$ R, S
Reason : $$F = qvB \Rightarrow {v^2} = {{{F^2}} \over {{q^2}{B^2}}}$$
Unit of v$$^2$$ is m$$^2$$s$$^{-2}$$ which to further equal to FV$$^2$$kg$$^{-1}$$
C $$	o$$ R, S
Reason : Escape velocity $${v_e} = \sqrt {{{2GM} \over R}} $$
$$v_e^2 = {{2GM} \over R}$$
The unit of $${{GM} \over R}$$ is $${m^2}{s^{ - 2}}$$
D $$	o$$ R, S

Answer

(A)→(P), (Q); (B)→(R), (S);
(C)→(R), (S); (D)→(R), (S)

Answer

(A)→(P); (B)→(R), (S);
(C)→(R), (S); (D)→(R)

Answer

(A)→(P), (Q); (B)→(S);
(C)→(R), (S); (D)→(S)

Answer

(A)→(Q); (B)→(R), (S);
(C)→(S); (D)→(R), (S)

Gravitation

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