1
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1 A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :
A
L $$\left( {1 + {2 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)$$
B
L $$\left( {1 + {1 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$$
C
L $$\left( {1 + {1 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)$$
D
L $$\left( {1 + {2 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$$
2
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1  Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :
A
$$x = r\left( {{H \over {H + h}}} \right)$$
B
$$x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 2}}}$$
C
$$x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 4}}}$$
D
$$x = r{\left( {{H \over {H + h}}} \right)^{{2}}}$$
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1 Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)
A B C D 4
JEE Main 2014 (Offline)
+4
-1
An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $$=76$$ $$cm$$ of $$Hg$$)
A
$$16$$ $$cm$$
B
$$22$$ $$cm$$
C
$$38$$ $$cm$$
D
$$6$$ $$cm$$
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