800 g lead balls are kept in a 1 m long, vertical tube which is a bad conductor and the tube is then closed at both ends. The tube is suddenly inverted so that the balls fall from one end to the other. The temperature of the lead balls increases by `3.89^(@)C` after 50 such inversions. Find out the mechanical equivalent of heat assuming that the lead balls have retained the entire amount of heat produced.

Explanation

Work done, W = loss of potential energy of the balls
`= n xx mgh`
`=50 xx 800 xx 980 xx 100 erg (1m^(.) = 100 cm)`
Heat produced, `H = mst = 800 xx 0.03 xx 3.89 cal`
`:. J = W/H = (50 xx 800 xx 980 xx 100)/(800 xx 0.03 xx 3.89) = 4.2 xx 10^(7) erg cdot cal^(-1)`.