AP EAMCET · PHYSICS · Mechanical Properties of Fluids
A cylindrical tank is filled with water to a level of \(3 \mathrm{~m}\). A hole is opened at a height of \(52.5 \mathrm{~cm}\) from the bottom. The ratio of the area of the hole to that of the cross-sectional area of the tank is 0.1 . The square of the speed with which water will be coming out from the orifice is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)
- A \(50 \mathrm{~m}^2 \mathrm{~s}^{-2}\)
- B \(40 \mathrm{~m}^2 \mathrm{~s}^{-2}\)
- C \(51.5 \mathrm{~m}^2 \mathrm{~s}^{-2}\)
- D \(50.5 \mathrm{~m}^2 \mathrm{~s}^{-2}\)
Answer & Solution
Correct Answer
(A) \(50 \mathrm{~m}^2 \mathrm{~s}^{-2}\)
Step-by-step Solution
Detailed explanation
Let \(a\) be area of hole, \(v_{\varepsilon}\) be the velocity of efflux, \(h\) be the height of liquid above the hole. Let \(v\) be the speed with which level decreases in the container. From equation of continuity, \[ a v_e=A v \Rightarrow v=\frac{a v_e}{A} \] Using…
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