Use the formula for Newton's law of universal gravitation:
#F_"grav"=(G*m_1*m_2)/d^2#,
where #G# is the universal gravitation constant, #m_1# is the mass of the first object in kg, #m_2# is the mass of the second object in kg, and #d# is the distance between them in meters.
Known
#G=(6.67xx10^(-11) "N"*"m"^2)/(kg^2")#
#m_1=35color(red)cancel(color(black)("mg"))xx(1color(red)cancel(color(black)("g")))/(1000color(red)cancel(color(black)("mg")))xx(1"kg")/(1000color(red)cancel(color(black)("g")))=3.5xx10^(-5)# #"kg"#
#m_2=21color(red)cancel(color(black)("mg"))xx(1color(red)cancel(color(black)("g")))/(1000color(red)cancel(color(black)("mg")))xx(1"kg")/(1000color(red)cancel(color(black)("g")))=2.1xx10^(-5)# #"kg"#
#d_1="8 m"#
#d_2="3 m"#
Unknown
Gravitational force, #F_"grav"#
Distance of 8 meters
#F_"grav"=(6.67xx10^(-11) ("N"*"m"^2)/"kg"^2xx3.5xx10^(-5)"kg"*2.1xx10^(-5)"kg")/(8"m"^2")#
Multiply the masses and square the distance.
#F_"grav"=(6.67xx10^(-11) ("N"*color(red)cancel(color(black)("m"^2)))/color(red)cancel(color(black)("kg"))^2xx7.35xx10^(-10)color(red)cancel(color(black)("kg"^2)))/(64color(red)cancel(color(black)("m"^2)))=7.7xx10^(-22)# #"N"#
Distance of 3 meters
#F_"grav"=(6.67xx10^(-11) ("N"*"m"^2)/"kg"^2xx3.5xx10^(-5)"kg"*2.1xx10^(-5)"kg")/(3"m"^2")#
Multiply the masses and square the distance.
#F_"grav"=(6.67xx10^(-11) ("N"*color(red)cancel(color(black)("m"^2)))/color(red)cancel(color(black)("kg"))^2xx7.35xx10^(-10)color(red)cancel(color(black)("kg"^2)))/(9color(red)cancel(color(black)("m"^2)))=5.4xx10^(-21)# #"N"#
Divide the force at 3 meters distance by the force at 8 meters distance.
#(5.4xx10^(-21)color(red)cancel(color(black)("N")))/(7.7xx10^(-22)color(red)cancel(color(black)("N")))=7.0#
The gravitational force increases 7 times when the distance between the objects decreases from 8 meters to 3 meters.
