Question

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

• A. 9 cm
• B. 6 cm
• C. 4.5 cm
• D. 2.25 cm

Answer 1

Answer: (B)

6 cm

Answer 2

The velocity of ball before entering the water surface

$v = \sqrt { 2 g h } = \sqrt { 2 g \times 9 }$

When ball enters into water, due to upthrust of water the velocity of ball decreases (or retarded)

The retardation, a = $\frac { \text { apparent weight } } { \text { mass of ball } }$

$= \left( \frac { 0.4 - 1 } { 0.4 } \right) \times g$ $= - \frac { 3 } { 2 } g$

If h be the depth upto which ball sink, then,

$0 - v ^ { 2 } = 2 \times \left( - \frac { 3 } { 2 } g \right) \times h$⇒ $2 g \times 9 = 3 g h$∴ h = 6 cm