Comprehension # 1 If net force on a system in a particular direction is zero (say in horizontal direction) we can apply: `Sigmam_(R )x_(R )= Sigmam_(L)x_(L), Sigmam_(R )v_(R )= Sigmam_(L)v_(L)` and `Sigmam_(R )a_(R ) = Sigmam_(L)a_(L)` Here R stands for the masses which are moving towards right and L for the masses towards left, x is displacement, v is veloctiy and a the acceleration (all with respect to ground). A small block of mass `m = 1 kg` is placed over a wedge of mass `M = 4 kg` as shown in figure. Mass m is released from rest. All surface are smooth. Origin O is as shown. Final velocity of the wedge is ..........`m//s` :-A. `sqrt3`B. `sqrt2`C. `(1)/(sqrt2)`D. `(1)/(sqrt3)`

Comprehension # 1 If net force on a system in a particular direction i

1.	Comprehension # 1 If net force on a system in a particular direction is zero (say in horizontal direction) we can apply: `Sigmam_(R )x_(R )= Sigmam_(L)x_(L), Sigmam_(R )v_(R )= Sigmam_(L)v_(L)` and `Sigmam_(R )a_(R ) = Sigmam_(L)a_(L)` Here R stands for the masses which are moving towards right and L for the masses towards left, x is displacement, v is veloctiy and a the acceleration (all with respect to ground). A small block of mass `m = 1 kg` is placed over a wedge of mass `M = 4 kg` as shown in figure. Mass m is released from rest. All surface are smooth. Origin O is as shown. Final velocity of the wedge is ..........`m//s` :-A. `sqrt3`B. `sqrt2`C. `(1)/(sqrt2)`D. `(1)/(sqrt3)`
Answer» Correct Answer - B By appplying conservation of momentum `mv_(1) + Mv_(2) = 0 rArr v_(1) = -4v_(2)` …..(i) By applying conservation of energy `(1)/(2)mv_(1)^(2) + (1)/(2)Mv_(2)^(2) = mgh rArr (v_(1)^(2))/(2) + 2v_(2)^(2) = 20` ……(ii) `v_(2) = sqrt2m//s , v_(1) = 4 sqrt2 m//s`.

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