Question

The area of the cross-section of a large tank is 0.5 m². It has a narrow opening near the bottom having an area of cross-section 1 cm². A load of 25 kg is applied to the water at the top of the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of the water level in the tank is 40 cm above the bottom, will be ______ cms^-1.

[Take g = 10 ms^-2]

पर्याय

• 100

• 200

• 300

• 400

Answer 1

The area of the cross-section of a large tank is 0.5 m². It has a narrow opening near the bottom having an area of cross-section 1 cm². A load of 25 kg is applied to the water at the top of the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of the water level in the tank is 40 cm above the bottom, will be 300 cms^-1.

Explanation:

By Bernoull's theorem,

`P + rhogh + 1/2rhoV^2` = constant

⇒ `(P_0 + (mg)/A) + rhogh = P_0 + 1/2rhoV^2` [∵ Speed of water in tank = 0]

⇒ `(25 xx 10)/0.5 + 1000 xx 10 xx 0.4 = 1/2 xx 1000 xx V^2`

⇒ 500 + 4000 = 500 V² ⇒ V² = 9

⇒ V = 3 m/s = 300 cm/sec