1
JEE Main 2018 (Offline)
+4
-1
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $$\left( {{dr \over r}} \right)$$ is:
A
$${{mg} \over {Ka}}$$
B
$${{Ka} \over {mg}}$$
C
$${{Ka} \over {3mg}}$$
D
$${{mg} \over {3Ka}}$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :
A
11.2 m
B
8.7 m
C
9.5 m
D
10.5 m
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is :
[kB =1.4 $$\times$$ 10-23 J/K; mHe = 7 $$\times$$ 10 -27 kg ]
A
1.3 $$\times$$ 104
B
1.3 $$\times$$ 103
C
1.3 $$\times$$ 105
D
1.3 $$\times$$ 102
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :
A
0.25 cm
B
0.37 cm
C
0.75 cm
D
1.00 cm
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