JEE Mains · Physics · STD 11 - 9.1 fluid mechanics
Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure) . Through a hole of radius \(r\) \((r << R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x.\) Then
- A \(x\, = \,r{\left( {\frac{H}{{H + h}}} \right)^{\frac{1}{4}}}\)
- B \(x\, = \,r\left( {\frac{H}{{H + h}}} \right)\)
- C \(x\, = \,r{\left( {\frac{H}{{H + h}}} \right)^2}\)
- D \(x\, = \,r{\left( {\frac{H}{{H + h}}} \right)^{\frac{1}{2}}}\)
Answer & Solution
Correct Answer
(A) \(x\, = \,r{\left( {\frac{H}{{H + h}}} \right)^{\frac{1}{4}}}\)
Step-by-step Solution
Detailed explanation
According to Bernoulli's principle, \(\frac{1}{2}\rho v_1^2 + \rho gh = \frac{1}{2}\rho v_2^2\) \(v_1^2 + 2gh = v_2^2\) \(2gH + 2gh = v_2^2\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\) \({a_1}{v_1} = {a_2}{v_2}\) \(\pi {r^2}\sqrt {2gh} = \pi {x^2}{v_2}\)…
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