The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be

(1). \(\displaystyle \frac{Mg}{2}\)
(2). \(Mg\)
(3). \( \frac{3}{2}\, Mg\)
(4). \(2\, Mg\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

Consider a water tank shown in the figure.It has one wall at x = L and can be taken to be very wide in the Z direction.When filled with a liquid of surface tension S and density P, the liquid surface makes angle \(\theta_0\).(\(\theta_0 \,<<\,1\)) with the x-axis at x = L. If y(x) is the height of the surface then the equation for y(x) is

(take \(\theta \left(\text{x} \right)\,=\, sin\theta \left(\text{x} \right)\,=\,tan\theta \left(\text{x} \right)\,=\, \frac{\text{dy}}{\text{dx}} \text{, g}\) is the acceleration due to gravity)

(1). \(\displaystyle \frac{\text{dy}}{\text{dx}}\,=\, \sqrt{\frac{\rho\text{g}}{\text{S}}x}\)
(2). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \frac{\rho \text{g}}{\text{S}}x\)
(3). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \frac{\rho \text{g}}{\text{S}}y\)
(4). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \sqrt{\frac{\rho \text{g}}{\text{S}}}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10mm above the water level on the other side. Mean while the water rises by 65 mm from its original level (see diagram). The density ofthe oil is


(1). \(650\, \text{Kg}\,m^{ −3}\)
(2). \(425\, \text{Kg} \,m^{−3}\)
(3). \(800\, \text{Kg}\, m^{ −3}\)
(4). \(928\, \text{Kg} \,m^{ −3}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02