MHTCET 13 May 2023 Shift 2 Solved Paper

Acceleration due to gravity of planet A is given below.
gA=‌

GMA

RA2

...(i)
∵ We know that, (Mass = Density × Volume )(M=D×V)
So, from Eq. (i)
‌gA=‌

GDA× 4 3 πRA3

RA2

=GDA×‌

4

3

πRA
‌gA=‌

4

3

πGRADA‌‌...‌ (ii) ‌...(ii)
Similarly, Acceleration due to gravity of planet B is gB=‌

GMB

RB2

..(iii)
and ‌‌gB=‌

4

3

πGDBRB....(iv)
We have to find the ratio of gA:gB
So, according to question, we have
‌

RA

RB

=‌

x

y

.....(v)
and ‌

DA

DB

=‌

m

n

...(vi)
Now, taking the ratio of Eqs. (ii) and (iv), we get
‌

gA

gB

=‌

RADA

RBDB

Put the value from Eqs. (v) and (vi) in this equation, we get
‌

gA

gB

=‌

x⋅m

y⋅n

or ‌‌gA/gB=mx/ny