A cylindrical tank, filled with water, has an area of 10m2. A piston covers its entire top surface. A uniformly distributed load of 1000N is applied on the piston from top. A hole of area 0.001m2is at the bottom of the tank. Find the speed of efflux when the height of water level is 0.1m .a)24.5m/sb)1.48m/sc)0.2m/sd)2m/sCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

To find the speed of efflux, we can apply Torricelli's theorem, which states that the speed of efflux through a small hole at the bottom of a container is given by the equation:

v = √(2gh)

where v is the speed of efflux, g is the acceleration due to gravity, and h is the height of the water level above the hole.

Given:
Area of the tank = 10 m^2
Load applied on the piston = 1000 N
Area of the hole = 0.001 m^2
Height of water level = 0.1 m

Step 1: Calculation of the force exerted by the water on the piston
The force exerted by the water on the piston is equal to the load applied on the piston. Since the load is uniformly distributed, the force exerted by the water can be calculated by dividing the load by the area of the piston.

Force exerted by the water = Load applied on the piston / Area of the piston

Force exerted by the water = 1000 N / 10 m^2

Force exerted by the water = 100 N

Step 2: Calculation of the pressure exerted by the water on the hole
The pressure exerted by the water on the hole can be calculated by dividing the force exerted by the water by the area of the hole.

Pressure exerted by the water = Force exerted by the water / Area of the hole

Pressure exerted by the water = 100 N / 0.001 m^2

Pressure exerted by the water = 100,000 Pa

Step 3: Calculation of the speed of efflux using Torricelli's theorem
Now, we can substitute the values into Torricelli's theorem to calculate the speed of efflux.

v = √(2gh)

v = √(2 × 9.8 m/s^2 × 0.1 m)

v = √(1.96 m^2/s^2)

v = 1.4 m/s

Therefore, the speed of efflux when the height of the water level is 0.1 m is approximately 1.4 m/s.

Hence, the correct answer is option 'B' - 1.48 m/s.

Answer

We should apply Bernoulli theorem between the top surface of water and the hole. The area of hole is very small when compared to the area of the tank. So, 1/2ρv² at the top surface of the tank can be neglected.
P₀ + F/AP + ρgh = P₀ + 1/2ρv²
∴ 1000/10 + 1000*10*0.1 = 0.5*1000 *v²
∴ v = 1.48m/s

Similar NEET Doubts

A uniform solid cylindrical roller of mass ‘m’ is being pulled on a horizontal surface with force F parallel to the surface and applied at its center. If the acceleration of the cylinder is ‘a’ and it is rolling without slipping then the value of ‘F’ is

Consider a sphere of radius R having charge Q uniformly distributed inside it at what minimum distance from its surface the electric potential is half of the electric potential as its centre?

Consider a sphere of radius R having charge q uniformly distributed inside it. At what minimum distance from its surface the electric potential is half of the electric potential at its centre ?

A charge Q is uniformly distributed throughout 25. the volume of a dielectric sphere of radius RI potential at its surface is 24 volts. Then potential R 3R 2 at r = and r= respectively are.?

Top Courses for NEETView all

Biology Class 11

Daily Test for NEET Preparation

NEET Mock Test Series 2025

Topic-wise MCQ Tests for NEET

Physics Class 11

Top Courses for NEET

Top Courses for NEET

Suggested Free Tests

Related Content

About NEET

NEET Preparation Material

How to Prepare for NEET Exam?

NCERT Based Study Material

NEET Mock Tests

Other Popular Exams

Company