Rubiks Cube with the Ping Pong Ball!

Classical Mechanics Level 4

Babu was crazy for his Rubiks cube and Ping pong ball. His mother was fed up with her son's Cube and the ball and one morning she threw his cube into water. Babu woke up and saw the cube was floating in water with 2cm of it above the water level. His mother then placed the ping pong ball of 100g on the surface of the cube and the cube went down from the surface of the water by 1cm. Then she challenged Babu that if he could determine the mass of the cube, she would give both the cube and the ball back to him. Otherwise he was not allowed to touch them again.

So, if u also love Rubiks Cube, help Babu to find out the mass of the cube so that he can get that back! Come on! Try! What's the mass of the Rubiks cube?


The answer is 254.

Anamul Babu by Anamul Babu , 24, Bangladesh

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1 solution

Anamul Babu
Oct 30, 2015

From Mr. Archimedes uncle,

1. m 1 g m_{1} g = V 1 ρ g V_{1} ρg

h 1 h_{1} = 2 CM

V 1 V_{1} = (x-2) x 34 x^{34}

m 1 = ρ ( x − 2 ) 2 m_{1} = ρ(x-2)^{2} ...... (1)

  1. When the Ball of 100 g is placed on the cube, weight m 2 = 100 + m 1 ; ( m 2 + 100 ) g = V 2 ρ g ; V 2 = x 3 ; m 2 + 100 = ρ x 3 m_{2} = 100+m_{1} ; (m_{2} + 100)g = V_{2}ρg ; V_{2} = x^{3}; m_{2} + 100 = ρx^{3}

  2. m 1 = m 2 ; ρ ( x − 2 ) 2 + 100 = ρ x 3 ; ρ = 1 g / c m 3 ; x = 50 m_{1} = m_{2}; ρ(x-2)^{2} + 100 = ρx^{3}; ρ= 1 g/cm^{3}; x= \sqrt{50}

Putting the value in equation no.1, we get m = 253.6 ~ 254 gm

1 Helpful 0 Interesting 0 Brilliant 0 Confused

m1 should be equal to p x^2 (x-2)

Akash singh - 5 years, 7 months ago

how do you get v1=(x-2)*x^34

Akash singh - 5 years, 7 months ago

i suppose answer should be 800 gm

Akash singh - 5 years, 7 months ago

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