Q10 of 42 Page 31

The motion of a particle of mass m is given by x = 0 for t < 0 s, x(t) = A sin4π t for 0 < t s, x(t) = A sin 4π t for 0 < t < (1/4) s (A > 0), and x = 0 for t > (1/4) s. Which of the following statements is true?

We have given mass=m, for t<0



Now let’s look for time interval



Also we know,


1st derivative of x(t) w.r.t. time will give velocity


⇒


2nd derivative of x(t) w.r.t. time will give velocity


⇒


Then,



Here, this force is obviously time dependent so force is not constant hence option (d) is correct.


Now let’s look to option (a) i.e. At t then



⇒


So from this we can say option (a) also correct.


Now for option (b) i.e. between t = 0 s and t = (1/4) s, as we know impulse is change in momentum or so at t = (1/4) s impulse will be


here we have to keep in mind that F(t) varies from t=0 to maximum 1/8 s, so F (1/4) will be replaced by F (1/8) also from above we have found



⇒ so option(b) is also correct.


Option (c) is absolutely wrong as we have above found that force is acting.


Option (e) is also wrong because we have already calculated the impulse.

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