and Mz are masses and R is a distance, what are the St units of the quantity M:,

Question

and Mz are masses and R is a distance, what are the St units of the quantity M:, ed by M2 divided by R2, that is ((Mi Ma)/R2)? Mi Mz have units kilograms R ((M: M-/R2)(kg kg/m2) Answer:((M; Mal/R) kg' m2 Remember that for a power o 1/a' (2) The Sl unit for force is the newton, [N]. One new ton equals one kilogram meter per second squared, that is N-kg m s2. In the equation F G (M, M2)/R'),G is New on's gravitational constant, F is a force and the other symbols are defined in problem (1). What are the Si units of G? IRemember factors can be moved to the other side of the equation Changing them to their reciprocals-flipping their powers' sigrs.] G "(kg m s 2Mkg) (kg) (m2 [Substituting the units of F,M1.2R. G kg1ms2 [Remember a' . Answer G kg ms2 (3) The vector R1 is 1.50X108 km i (a) Express the x component of Ri in meters. Rx 1.50X10" km [Remember i is the unit vector in the x direction so its coefficient is the x component.] Ru = 1.50X1 X103 m = 1.50X10°.3 m Answer: R1.50X1011 m

Explanation / Answer

1. given vector

R = 1.1*10^11 i m + 1.1*10^11 m

hence

|R| = 1.1810^11 *sqrt(2) = 1.67*10^11 m

2. M1 = 2*10^33g

M2 = 6.0*10^27 g

G = 6.7*10^-11kg-1m3s^-2

R = 1.67*10^11

hence

F= GM1M2/R^2 = 288.2857*10^20 N

3. Rm = 85*10^9 m i

R = 1.1*10^11(i + j) m

F = 288.2857*10^20 N ( i + j )/sqrt(2) N ALONG TH ERDIRECITON OF VECtor R

and

Rm wrt sun = R + Rm =(1.95i + 1.1j)*10^11 m

|Rms| 2.2388613*10^11 m

4. as mass of sun is huge

hence

M = 2*10^30 kg

so, T = 2*pi*|Rms|/v

and

GM/|Rms| = v^2

T = 2*pi*|Rms|*sqrt(|Rms|/GM) = 1.821841120 years

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