1
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium position, taken to be at $$x=0,$$ with an amplitude $$A$$. An electric field $$E$$ is applied along the $$x$$-direction. Which of the following statements is correct ?
A
The new equilibrium position is at a distance $${{qE} \over {2k}}$$ from $$x=0.$$
B
The total energy of the system is $${1 \over 2}m{\omega ^2}{A^2} + {1 \over 2}{{{q^2}{E^2}} \over k}.$$
C
The total energy of the system is $${1 \over 2}m{\omega ^2}{A^2} - {1 \over 2}{{{q^2}{E^2}} \over k}.$$
D
The new equilibrium position is at a distance $${{2qE} \over k}$$ from $$x=0.$$
2
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $${27^ \circ }C.$$ The work done on the gas will be :
A
$$300$$ $$R$$
B
$$300$$ $$R$$ $$ln$$ $$6$$
C
$$300$$ $$R$$ $$ln$$ $$2$$
D
$$300$$ $$R$$ $$ln$$ $$7$$
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common interface and the vertical is :
A
$$\theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$
B
$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)$$
C
$$\theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)$$
D
$$\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)$$
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Take the mean distance of the moon and the sun from the earth to be $$0.4 \times {10^6}$$ km and $$150 \times {10^6}$$ km respectively. Their masses are $$8 \times {10^{22}}$$ kg and $$2 \times {10^{30}}$$ kg respectively. The radius of the earth is $$6400$$ km. Let $$\Delta {F_1}$$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $$\Delta {F_2}$$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $${{\Delta {F_1}} \over {\Delta {F_2}}}$$ is :
A
$$2$$
B
$${10^{ - 2}}$$
C
$$0.6$$
D
$$6$$
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