 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2012

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times {10^{ - 2}}\,\,N$ (see figure). The length of the slider is $30$ $cm$ and its weight negligible. The surface tension of the liquid film is A
$0.0125\,\,N{m^{ - 1}}$
B
$0.1\,\,N{m^{ - 1}}$
C
$0.05\,\,N{m^{ - 1}}$
D
$0.025\,\,N{m^{ - 1}}$

Explanation

At equilibrium,
$2Tl = mg$
$T = {{mg} \over {2l}} = {{1.5 \times {{10}^{ - 2}}} \over {2 \times 30 \times {{10}^{ - 2}}}} = {{1.5} \over {60}}$
$= 0.025\,N/m = 0.025Nm$
2

AIEEE 2011

Water is flowing continuously from a tap having an internal diameter $8 \times {10^{ - 3}}\,\,m.$ The water velocity as it leaves the tap is $0.4\,\,m{s^{ - 1}}$ . The diameter of the water stream at a distance $2 \times {10^{ - 1}}\,\,m$ below the tap is close to :
A
$7.5 \times {10^{ - 3}}m$
B
$9.6 \times {10^{ - 3}}m$
C
$3.6 \times {10^{ - 3}}m$
D
$5.0 \times {10^{ - 3}}m$

Explanation

From Bernoulli's theorem,
${P_0} + {1 \over 2}\rho v_1^2\rho gh = {P_0} + {1 \over 2}\rho v_2^2 + 0$
${v_2} = \sqrt {v_1^2 + 2gh}$
$= \sqrt {0.16 + 2 \times 10 \times 0.2}$
$= 2.03\,m/s$
From equation of continuity
${A_2}{v_2} = {A_1}{v_1}$
$\pi {{D_2^2} \over 4} \times {v_2} = \pi {{D_1^2} \over 4}{v_1}$
$\Rightarrow \,\,{D_1} = {D_2}\sqrt {{{{v_1}} \over {{v_2}}}} = 3.55 \times {10^{ - 3}}m$
3

AIEEE 2011

Work done in increasing the size of a soap bubble from a radius of $3$ $cm$ to $5$ $cm$ is nearly (Surface tension of soap solution $= 0.03N{m^{ - 1}},$
A
$0.2\pi mJ$
B
$2\pi mJ$
C
$0.4\pi mJ$
D
$4\pi mJ$

Explanation

$W = T \times \,\,$ change in surface area
$W = 2T4\pi \left[ {{{\left( 5 \right)}^2} - {{\left( 3 \right)}^2}} \right] \times {10^{ - 4}}$
$= 2 \times 0.03 \times 4\pi \left[ {25 - 9} \right] \times {10^{ - 4}}\,J$
$= 0.4\pi \times {10^{ - 3}}\,J$
$= 0.4\pi mJ$
4

AIEEE 2010

A ball is made of a material of density $\rho$ where ${\rho _{oil}}\, < \rho < {\rho _{water}}$ with ${\rho _{oil}}$ and ${\rho _{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?
A B C D Explanation

Oil will float on water so, $(2)$ or $(4)$ is the correct option, But density of ball is more than that of oil, hence it will sinkin oil.