Two carts of masses 200 kg and 300 kg on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the 200 kg cart travels a distance of 36 m and stops, then the distance travelled by the cart weighing 300 kg is 

(1) 32 m

(2) 24 m

(3) 16 m

(4) 12 m

Concept Videos :-

#16-Static-Friction-Force
#17-Solved-Examples-8
#18-Solved-Examples-9
#19-Solved-Examples-10
#20-Kinetic-Friction-Force
#21-Solved-Examples-11

Concept Questions :-

(3)

Let velocity of both carts be v1 and v2 just after the separation.

By conservation of momentum-

m1v1 =m2v2v1 v2  =m2m1Final velocity of each block is zero. Let the stopping be s1 and s2 for both the blocks.Using 3rd equation of motion -0 =v12 - 2as1 s1 =v122a Also, retardation of both blocks is a =μgs2 =v222aso, s1s2 =v12 v22 =m2m12So, s1m2

s2s1=m1m22=2003002

s2=s1×49=36×49=16m 

Difficulty Level:

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