Question

A metal ball weighs 9500 N in air and 8000N in water.Find volume and specific gravity

Answer 1

w =mg . apply this ..

Answer 2

Weight of ball in air = 9500 N

Weight of ball in water = 8000 N

Difference of weights = 9500 - 8000 = 1500 N

Now this difference of weight is Buoyant Force

Buoyant Force (In water ) = density of water * g * volume of body

(Taking g = 9.8 m/s²  and

density of water = 1* 10³ kg/ m³)

Substituting the values on the formula we get ;

1500 = 1* 10³ * 9.8 * volume of body

Volume of body = $\frac{1500}{1000*9.8}$

Volume of body = 0.15 m³

Now,

Weight of body in air [mg] = 9500 N

(where, m is the mass and g is gravity)

Hence,

mg = 9500 N

Thus mass of body [ m ] = 9500 / 9.8 kg = 969.39

Mass of body [ m ] =  969.39 kg

So,

Density of body = mass of body / volume of body

D = 969.39 / 0.15

D = 6462.5 kg / m³

Now density for body = 6462.5 kg/m³ and

density for body = 1000 kg/m³

Specific gravity is given by;

Specific gravity = Density of body / Density of water

Substituting the values of densities,

Specific gravity = 6462.5 / 1000

Specific gravity = 6.46

Hence,

The volume of body is  0.15 m³

The Specific gravity is 6.46