On dipping a capillary of radius 'r' in water, water rises upto a height H and potential energy of water is u1. If a capillary of radius 2 r is dipped in water, then the potential energy is u 2. The ratio ( u 1/ u 2) is

Question

On dipping a capillary of radius 'r' in water, water rises upto a height H and potential energy of water is u1. If a capillary of radius 2 r is dipped in water, then the potential energy is u 2. The ratio ( u 1/ u 2) is (A) 2: 1 (B) 1: 2 (C) 4: 1 (D) 1: 1

Tardigrade Admin · Accepted Answer

PE = mgh ∵ m propto r and h propto (1/ r ) ⇒ PE does not depends on r.

Q. On dipping a capillary of radius 'r' in water, water rises upto a height $H$ and potential energy of water is $u_{1}$ . If a capillary of radius $2 r$ is dipped in water, then the potential energy is $u_{2}$ . The ratio $\frac{u _{1}}{u _{2}}$ is

2 : 1

1 : 2

4 : 1

1 : 1

$PE = m g h$
$∵ m \propto r$ and $h \propto \frac{1}{r}$
$\Rightarrow$ PE does not depends on $r$ .

Q. On dipping a capillary of radius 'r' in water, water rises upto a height H and potential energy of water is u1​. If a capillary of radius 2r is dipped in water, then the potential energy is u2​. The ratio u2​u1​​ is