Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of- (density of water = 1000 kg/$m^3$, coefficient of viscosity of water = 1 m Pa s)
1.  ${10}^4$
2. ${10}^3$
3. ${10}^2$
4.  10

If \(M\) is the mass of water that rises in a capillary tube of radius \(r,\) then mass of water which will rise in a capillary tube of radius \(2r\) is:
1. \(M\)
2. \(4M\)
3. \(M/2\)
4. \(2M\)
 

A wooden block is initially floating in a bucket of water with \(\frac{4}{5}\)​ of its volume submerged. When a certain amount of oil is poured into the bucket, the block is found to be just under the oil surface with half of its volume submerged in water and half in oil. What is the density of the oil relative to that of water?
1. \(0.7\)
2. \(0.5\)
3. \(0.8\)
4. \(0.6\)

Water from a tap emerges vertically downwards with an initial speed of \(1.0~\text{m/s}\). The cross-sectional area of the tap is \(10^{-4}~\text{m}^2\). Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, \(0.15~\text{m}\) below the tap would be: (Take \(g=10~\text{m/s}^2\))
1. \(5\times10^{-4}~\text{m}^2\)
2. \(2\times10^{-5}~\text{m}^2\)
3. \(5\times10^{-5}~\text{m}^2\)
4. \(1\times10^{-5}~\text{m}^2\)

A submarine experiences a pressure of 5.05 × 10⁶ Pa at a depth of d₁ in a sea. When it goes further to a depth of d₂, it experiences a pressure of 8.08 × 10⁶ Pa. Then d₂ - d₁ is approximately: (density of water = 10³ kg/m³ and acceleration due to gravity = 10 ms^–2)
1.  600 m
2. 400 m
3. 300 m
4. 500 m

A cubical block of side \(0.5\) m floats on water with \(30\)% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it underwater?
(take, density of water \(=10^3\) kg/m³⁾
1. \(30.1\) kg
2. \(87.5\) kg
3. \(65.4\) kg
4. \(46.3\) kg

A solid sphere, of radius \(R, \) acquires a terminal velocity \(v_1\) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta.\)$$ The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(v_2\), when falling through the same fluid, the ratio \(\left(\dfrac{v_1}{v_2}\right) \) equals:
1. \(\dfrac{1}{9}\)
2. \(\dfrac{1}{27}\)
3. \(9\)
4. \(27\)