wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A ball whose density is 0.4×103kg/m3 falls into water from a height of 9cm. To what depth does the ball sink.

A
9cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
6cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4.5cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2.25cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 6cm
The ball is dropped from a height of h0=9cm. The velocity of the ball just before entering the water surface will be v0=2gh0, where h0=9cm=0.09m
After entering into the water with velocity v0, the buoyant force will work on it in opposite direction, and will stop it's motion. The net force on ball under water will be Fnet=Buoyant force - weight of ball=V×ρ×gV×σ×g
Fnet=Vg(ρσ)
Where ρ and σ are the densities of water and ball respectively.
Fnet force will work in the opposite direction of motion of the ball and will give retardation of a
Where a=Fnetm= (FnetVσ)=Vg(ρσ)Vσ=(ρσ1)g
By putting the density of water is ρ=103kg/m3 and the density if ball is σ=0.4×103kg/m3 in above equation we get,
a=1.5g
By using a third equation of motion we can write v2=u22ah, where v is the final velocity of ball under water, u is initial velocity of ball under water and h is the depth covered by ball in the water, a is the retardation due to net force working in opposite direction.
Due to retardation, the ball will stop eventually at some depth h, hence the final velocity of the ball under water v=0, and initial velocity of a ball under water is same as v0, so u=v0
Hence we can write h=(v0)22a, a=1.5g and v0=2gh0
By putting all the given values in the above equation we get,
h=2h03
h=2×9cm3=6cm
Hence Correct answer is B.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Kepler's Law
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon