Question

A cubical block of wood of edge $3cm$ floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. The maximum weight that can be put on the block without wetting it is :

(Density of wood$=800kg/m^3$ and spring constant of the spring $=50N/m$. Take g$=10m/s^2$ )

• A. $0.35N$
• B. $0.55N$
• C. $0.65N$
• D. $0.75N$

Answer 1

The correct option is A $0.35N$

Density of the wood$=800kg/m^3$

volume of cube $=27c{m}^3$

weight of cube $=0.8\times 27gms$

$=21.6gms$

let height of cube dipped in water be $h$,

for equilibrium,

weight of water displaced= weight of cube

$=9h\times 1000=21.6$

$h=\frac{21.6}{9}cms=2.4cms$

let maximum weight on that can be put on the cube without actually wetting it is $w$

balancing the forces, $w+\frac{21.6\times 10}{1000}=\frac{27}{1000}\times 10+50\times \frac{0.6}{100}$

$\to W=0.27-0.216+0.3$

$w=0.354N$

$W\approx 0.35N$