1
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Consider a solid sphere of radius R and mass density
$$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$ , $$0 < r \le R$$
The minimum density of a liquid in which it will float is :
A
$${{2{\rho _0}} \over 3}$$
B
$${{2{\rho _0}} \over 5}$$
C
$${{{\rho _0}} \over 5}$$
D
$${{{\rho _0}} \over 3}$$
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :
A
1.04
B
1.26
C
1.01
D
1.03
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :
A
$${3 \over 4}$$
B
$${9 \over {16}}$$
C
$${{\sqrt 3 } \over 2}$$
D
$${{81} \over {256}}$$
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio (v1/v2) equals :
A
$${1 \over 9}$$
B
$${1 \over {27}}$$
C
27
D
9
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