Question

A stone of relative density k is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of 

Solution

Correct option is

 

If m is the mass of the stone and V its volume, the weight of the water displaced by it =  is the density of water. Therefore, . Thus, the buoyant force acting upwards is mg/kwhereas the weight mg of the stone acts vertically downwards. Therefore, the net force in the downward direction . If is the acceleration of the sinking stone, then 

        

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SIMILAR QUESTIONS

Q1

A cubical vessel of height 1 m is full of water. What is the amount of work done is pumping water out of the vessel? Take g = 10ms–2 

Q2

The dimensions of viscosity in terms of M, L and T are

Q3

The dimensions of Reynold’s number are

Q4

A rain drop of radius r falls in air with a terminal speed vt. What is the terminal speed of a rain drop of radius 2r

Q5

Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms–1. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.

Q6

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is 2v being the density of water?    

Q7

The cylindrical tube of a spray pump has a radius R, one end of which hasn fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is 

Q8

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the lower and upper surfaces of the wing are v and  respectively. If the density of air is  and the surface area of the wing is A, the dynamic lift on the wing is given by     

Q9

A piece of copper having an internal cavity weights 264 g in air and 221 g in water. The density of copper is 8.8 gm–3. What is the volume of the cavity?

Q10

Two identical cylindrical vessels, each of base area A, have their bases at the same horizontal level. They contain a liquid of density . In one vessel the height of the liquid is h1 and in the other h2 > h1. When the two vessels are connected, the work done by gravity in equalizing the levels is