IAS 2021 — CSAT Maths

Correct Option (C)

The initial height from which the ball is dropped is 1.5 m, which is equivalent to 150 cm.

The ball bounces back to 4/5^th of its previous height. The criterion for the ball to cease bouncing is when the height attained in the previous bounce is less than 50 cm.

• After the 1^st impact with the ground, the ball bounces to a height of $\frac{4}{5} \times 150 \text{ cm} = \textbf{120 cm}$54​×150 cm=120 cm.
• After the 2^nd impact, the ball bounces to a height of $\frac{4}{5} \times 120 \text{ cm} = \textbf{96 cm}$54​×120 cm=96 cm.
• After the 3^rd impact, the ball bounces to a height of $\frac{4}{5} \times 96 \text{ cm} = \textbf{76.8 cm}$54​×96 cm=76.8 cm.
• After the 4^th impact, the ball bounces to a height of $\frac{4}{5} \times 76.8 \text{ cm} = \textbf{61.44 cm}$54​×76.8 cm=61.44 cm.
• After the 5^th impact, the ball bounces to a height of $\frac{4}{5} \times 61.44 \text{ cm} = \textbf{49.152 cm}$54​×61.44 cm=49.152 cm.

Since the height attained after the 5^th impact (49.152 cm) is less than 50 cm, the ball will not bounce further after its 6^th impact with the ground. Consequently, the ball hits the ground a total of 6 times before it stops bouncing.

Incorrect Options:

Options A (4), B (5), and D (7) are incorrect. The sequential calculation of bounce heights demonstrates that the ball continues to bounce until the height achieved after the 5^th impact falls below the 50 cm threshold. This condition is met at 49.152 cm, implying that the ball will undergo a 6^th and final impact before ceasing to bounce. Therefore, selecting 4 or 5 would prematurely conclude the counting of impacts, while 7 would incorrectly suggest an additional bounce beyond the established stopping condition.