A particular block floats in water at 4^(@)C so that 0.984 of its height is under water. At what temperature, will it just sink in water? Neglect expansion of block. (Volume coefficient of expansion of water =2.1 xx 10 ^(-4) per ^(@)C)

A particular block floats in water at 4^(@)C so that 0.984 of its heig

1.	A particular block floats in water at 4^(@)C so that 0.984 of its height is under water. At what temperature, will it just sink in water? Neglect expansion of block. (Volume coefficient of expansion of water =2.1 xx 10 ^(-4) per ^(@)C)
Answer» Solution :` d _(t) = (d _(0))/( 1 + GAMMA t ) , d _(0) = 1 GM//c.c ,d _(t) = 0.984 gm //c.c,` The block sinks when the density of the block and the water are just equal. `therefore 0.984 = (1)/( 1 + 2.1 xx 10 ^(-4) t ) therefore 1 + 2.1 xx 10 ^(-4) t = (1)/( 0.984) = (1000)/(984) = (500)/(492)` `therefore 2.1 xx 10 ^(-4) t = (8)/( 492),t = ( 8xx 10 ^(4))/( 492 xx 2.1) = 77.43 ^(@)C,` It MUST be heated to `77.43+4 = 81.43 ^(@)C`