1
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1 A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi$$kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?
A
$${{\Delta \gamma } \over \gamma }$$ gets minimum contribution from the uncertainty in the length.
B
The figure of merit is the largest for the length of the rod.
C
The maximum value of $$\gamma$$ that can be determined is 2 $$\times$$ 1014 N/m2
D
$${{\Delta \gamma } \over \gamma }$$ gets its maximum contribution from the uncertainty in strain
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1 A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta$$a) where ($$\Delta$$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $$\mu$$ then the force needed to push the cork into the bottle is : A
($$\pi$$ $$\mu$$ B b) $$\Delta$$a
B
(2$$\pi$$ $$\mu$$ B b) $$\Delta$$a
C
($$\pi$$ $$\mu$$ B b) a
D
(4$$\pi$$ $$\mu$$ B b) $$\Delta$$a
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1 A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $$\alpha$$ then the value of S is :
A
$$\alpha$$
B
$${\alpha \over 2}$$
C
2$$\alpha$$
D
$${1 \over \alpha }$$
4
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 $$\left( {1 + {2 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$$
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