Question

A wooden block, with a coin placed on its top, floats in water as shown in the fig. The distance \[l\] and \[h\] are shown there. After some time the coin falls into the water, then

A. \[l\] decreases and \[h\] increases
B. \[l\] increases and \[h\] decreases
C. Both \[l\] and \[h\] increases
D. Both \[l\] and \[h\] decreases

Answer 1

Hint:Observe the force acting on the combined system of wooden block and the coin. Check how the force on the system changes when the coin falls into the water and how it affects the water level. According to that select the option which fits the situation.

Complete answer:
Given, a wooden block floats in water and a coin is placed at the top of the wooden block.
\[l\] is the height of the wooden block that is underwater and \[h\] is the height of the water.
We are asked what will happen to the length \[l\] and \[h\] when the coin falls into the water.

Let \[m\]be the mass of the coin and \[M\] be the mass of the wooden block. Gravitational force is acting on the wooden block and the coin downwards with acceleration due to gravity \[g\]. The weight of coin will be \[{W_c} = mg\] and weight of the wooden block will be \[{W_b} = Mg\]
Combined weight will be \[W = Mg + mg\]

When a body falls in a liquid it displaces some amount of liquid comparable with the body’s weight.Here, the coin is not so massive, so when the coin falls into the water it displaces negligible amounts of water.One more important concept is buoyant force or upthrust which is the force exerted by the liquid on the object in upward direction, opposite to the gravitational force.

So, when the coin falls into the water combined weight decreases thus the force acting downwards too decreases which in turn increases the upthrust and the wooden block lifts up that means the part of the wooden block under the water decreases and also the water level goes down that means height of the water decreases.

Hence, the correct answer is option D.

Note:When a body floats on liquid, its weight decreases this is due to buoyancy. Buoyancy is the force which acts opposite to that of gravity and lets a body to float. But when the weight of the body is large, that is, the gravitational force is large compared to the buoyant force then it sinks in the liquid.