Bullet fires with velocity u; after 24 cm velocity = u/3. Then comes to rest at end of block. Find total length.

Step-1: Find retardation (v² = u² − 2as):

(u/3)² = u² − 2a(0.24)

u²/9 = u² − 0.48a

0.48a = u²(1 − 1/9) = 8u²/9 ⇒ a = 50u²/27

Step-2: Additional distance to stop from v = u/3:

0 = (u/3)² − 2a·s₂

s₂ = (u²/9) / (2 × 50u²/27) = (u²/9) × (27/100u²) = 0.03 m = 3 cm

Step-3: Total length:

L = 24 cm + 3 cm = 27 cm

Answer: Total length of the block = 27 cm