A rubber ball of mass 10 g and radius 2 cm is submerged in water up to a depth of 5 cm and released. Find the height up to which the ball pops up above the surface of water, neglecting the resistance of water and air. The density of water = `1g*cm^(-3)`.
Text Solution
Verified by Experts
Volume of the rubber ball, `V=4/3xx22/7xx(2)^(3)cm^(3)=704/21cm^(3)` Resultant upward force = buoyant force - weight of the rubber ball or, `10a=Vxx1xxg-10xxg" "`[a = upward acceleration] or, `10a=(704g)/21-10gor,a=494/210gcm*s^(-2)` Let the velocity of the ball when it reaches the surface of water be v, then `v=sqrt(2as)=sqrt((2xx494)/210xx980xx5)` `=sqrt((2xx494xx14xx5)/3)=151.83cm*s^(-1)` If the ball pops up to a height x above the surface of water, then `v^(2)=2gxor,x=v^(2)/(2g)=((151.83)^(2))/(2xx980)=11.76cm`.
Topper's Solved these Questions
HYDROSTATICS
CHHAYA PUBLICATION|Exercise SECTION RELATED QUESTIONS|12 Videos
HYDROSTATICS
CHHAYA PUBLICATION|Exercise HIGHER ORDER THINKING SKILL (HOTS) QUESTIONS|37 Videos
FRICTION
CHHAYA PUBLICATION|Exercise CBSE SCANNER|7 Videos
KINETIC THEORY OF GASES
CHHAYA PUBLICATION|Exercise CBSE Scanner|9 Videos
Similar Questions
Explore conceptually related problems
A cistern 6 m long and 4 m wide, contains water up to a depth of 1m 25 cm. The total area of the wet surface is______
A rubber ball of mass 100 g falls from a height of 1 m rebounds to a height of 40 cm. Find the impulse and the average force between the ball and the ground if time during which they are in contact was 0.1 s.
Calculate the pressure at the bottom of a fresh water lake of depth 10 m. The atmospheric pressure = 76 cm of mercury and the density of mercury = 13.6g*cm^(-3) .
When a body of mass 200 g is placed on a wooden cube, the cube floats completely immersed in water. When the body is removed, the cube floats up 2 cm above the surface of the water. What is the volume of the cube?
Find the pressure inside on air bubble of radius 0.1 mm just inside the surface of water. Surface tension of water = 72 dyn. cm^-1 .
From the two arms of a beam balance, a metal body weighing 20 g and a piece of glass are suspended. The apparent weights of these two bodies when measured in water are found to be the same. If immersed in alcohol instead of water, the mass of the metal needs to be increased by 0.84 g for balancing the beam. Calculate the mass of the glass piece. [Given, density of water = 1g*cm^(-3) , density of alcohol = 0.96g*cm^(-3) ]
A cylinder of radius 12 cm contains water to a depth of 20 cm. When a spherical iron ball is dropped in to the cylinder, the level of water is raised by 6.75 cm. Find the radius of the ball. [pi = (22)/(7)]
Each side of an iron cube is 5 cm. This cube floats on mercury. What height of the cube remains above the surface of mercury? To cover the cube, if water is poured over mercury, then what will be the height of the water column? The density of iron is 7.2g*cm^(-3) and the density of mercury is 13.6g*cm^(-3) .
A source of light is placed at the bottom of a tank filled with water up to the height of 80 cm. Calculate the area at the surface of water through which light rays will be emitted. Refractive index of water = 1.33.
