try to solve this question please can you help me Option 1 A1.200Kg crate is sun

Question

try to solve this question please can you help me

Option 1 A1.200Kg crate is sunk in the harbor and sits on the bottom a depth of 30m. The crate is square and measures 3m on each side Aplan to raise the boat using ping pong balls has been put in place. The boat is sealed so that the ping pong balls can be added to the boat and will remain in the boat displacing enough water to raise it to the surface. An average ping pong ball is 4 cm in diameter. Ping Pong balls have a typical mass of 2.7g and 0.2% of them are poorly made and will take on water. How ou need? Can you fit than man n the crate many W

Explanation / Answer

in order to raise the crate back, buoyancy force should be equal to weight of crate + weight of ping pong balls

if n= no of ping pong balls used,then 98% only will help

then volume of ping pong ball= 0.98 n x (4/3) x 3.141 x (0.02)^3 0.02 is radius of ping pong ball

buoyancy force= density of water x volume displaced x g

= 1000 x 0.98n x (4/3) x 3.141 x (0.02)^3 x 9.8

this buoyancy force should be equal to weight of crate + weight of ping pong ball

= 1200 x 9.8 + n x2.7 x 10^-3 x 9.8

so, 1200 x 9.8 + n x2.7 x 10^-3 x 9.8 = 1000 x 0.98n x (4/3) x 3.141 x (0.02)^3 x 9.8

so, n= 39,832

so no of ping pong balls= 39,832

volume of crate= 3x3x30= 270 m^3

volume of 1 ping pong ball= (4/3) x 3.141 x (0.02)^3= 0.000033504 m^3

so no of balls crate can fit= 8058739

which is very high compared to 39,832

hence, we can fit all the ping pong balls

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