9. Two skaters stand face-to-face on the ice. Skater 1 has a mass of 40 kg, and

Question

9. Two skaters stand face-to-face on the ice. Skater 1 has a mass of 40 kg, and skater 2 has a mass of 50 kg. The push off one another and move in opposite directions. What is the ratio of skater 1's speed to skater 2's speed? (d) 5:4 10. Consider the force F shown in the Figure 3. This force acts on an object that can move along the positive or negative axis, or along the positive or negative y axis. The work done by this force is positive when the displacement of the object is along which pair of axes or directions? (a) -x and -y (b) -x and ty (c) +x and +y x and -y

Explanation / Answer

Sol 9:

Using conservation of momentum (since no external force is applied here the momentum of the system should be conserved), momentum before push = momentum after push

momentum, p=m*v

let velocity of 40 kg person after push be v1 and that of 50 kg person be v2 after the push

pbefore=pafter

(40*0)+(50*0)=(40*v1)+(50*v2)

from above, v1/v2= -5/4

here '-' represents that both the velocities are in opposite direction.

hence ration of speeds is v1/v2=5/4

so option d is correct.

Solution 10:

From figure we can say that force is the form of, F=(-xi+yj) {since it is in -ve x and +ve y}

Now we know work is dot product of force and displacement

W=F.d=(-xi+yj).d

for work to be positive d should lie in -ve x and postive y so as to make the dot product of both positive.

hence, option b is correct.

To check you can assume d=(-ai+bj)

Now dot product becomes (a*x i+ b*y j) which is positive.

In the same way you can assume different values of d to check

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