A carriage of mass M and length ℓ is joined to the end of a slope as shown in the figure. A block of mass m is released from the slope from height h . It slides till end of the carriage. The friction

Question

A carriage of mass M and length ℓ is joined to the end of a slope as shown in the figure. A block of mass m is released from the slope from height h . It slides till end of the carriage. The friction between the mass and the slope and also friction between carriage and horizontal floor is negligible. Coefficient of friction between block and carriage is μ . Find h in the given terms.

TestHub · Accepted Answer

Finally m g h = 2 1 ​ m v 2 P i ​ = P f ​ . m v = ( M + m ) v ′ v ′ = M + m m v ​ ​ − μ m g ℓ = 2 1 ​ ( M + m ) v ′2 − 2 1 ​ m v 2 μ m g ℓ = 2 1 ​ m v 2 − 2 1 ​ ( m + M ) ( ( m + M ) 2 m 2 v 2 ​ ) μ m g ℓ = 2 1 ​ ( m + M m M ​ ) v 2 μ m g ℓ = ( m + M M ​ ) m g h h = μ ( M m + M ​ ) ℓ ​ .

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JEE Main 2027 (Class 12)