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

2. \(10^3\)${\mathrm{}}^{}$

3. \(10^2\)${\mathrm{}}^{}$

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. \(2M\)

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: