A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000\, kg$. The area of cross section a of piston carrying the load is $425\, cm ^{2}$. What is the maximum pressure () would smaller piston have to bear ?
$15.82 \times 10^{5} Pa$
$1.12 \times 10^{5} Pa$
$2.63 \times 10^{5} Pa$
$6.92 \times 10^{5} Pa$
A boy carries a fish in one hand and a bucket(not full) of water in the other hand . If he places the fish in the bucket , the weight now carried by him (assume that water does not spill) :
A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 p$. The complete arrangement is placed in a liquid of density $2 p$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are)
$(A)$ the net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ the net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ the light sphere is partially submerged.
$(D)$ the light sphere is completely submerged.
A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is
Write the only equation for the volume of partially immerged part of body float on the surface of liquid.
The spring balance $A$ reads $2\, kg$ with a block m suspended from it. $A $ balance $B$ reads $5 \,kg $ when a beaker filled with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid as shown in figure. In this situation