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A block of mass 2 kg is free to move alo...

A block of mass `2 kg` is free to move along the `x`-axis. It at rest and from `t = 0`onwards it is subjected to a time-dependent force `F(t)` in the `x` direction. The force `F(t)` varies with `t` as shown in the figure. The kinetic energy of the block after `4.5` seconds is

A

4.50 J

B

7.50 J

C

5.06 J

D

14.06 J

Text Solution

Verified by Experts

The correct Answer is:
C
Area under the F-t graph is equal to appled impulse on the block which is equal to change in its linear momentum .
Let `F_(0)` be the magnitude of maximum force in negative direction .
`(F_(0))/(1.5) = 4/3 rArr F_(0) = 2N `
Impulse = Area under the graph
`1/2 xx 4xx 3 - 1/2 xx2xx1.5 = 6-1.5 = 4.5 Ns `
Change in linear momentum = Impulse
Since initial momentum is zero hence change in momentum is same as final momentum (p)
`rArr p = 4.6 Ns`
Kinetic energy ` = (p^(2))/(2m) = (4.5 xx4.5)/(2xx2) =5.06 J `
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Knowledge Check

  • A block of mass 2 kg is free to move along the x-axis it is at rset and from t=0 onwards it is subjected to a time dependent force F(t) in the x-direction The force F(t) varies with t as shown in the figure The kinetic energy of the block after 4.5 seconds, is:

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