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1) A body of mass m has its position x at a time t expressed by the equation x = 3t^(3/2) + 2t^(-1/2). The instantaneous force on the body is proportional to
[i] t^0 [ii] t^(-3/2) [iii]t [iv]t^(3/2)
2) A fat hose pipe is held horizontal by a fireman. It delivers water through a nozzle at one litre/sec. If by increasing the pressure, the water is delivered at 2 litre/sec, the fireman now has to:[i] push forward twice as hard
[ii] push forward four times as hard
[iii] push forward eight times as hard
[iv] pull backward four times as hard
3) Is physical independence of force a consquence of first law of motion? If yes, the why is it so?
Please reply ASAP. Thank you!
A)In instaneous force Lim (t->0) dP/dt . if u derivate the given equation two times you will get t powers as negative . so after apply limit to the equation force is directly proportional to t^0.
So ans is option A
for instantaneous force
formula is
Lim(t-->0)(m*a)
where a=d^2(x)/dt^2
then if you derivate the given displament equation you wiil get answer negative power of t
and then apply the limit value of t=0
then i.e proportional to t^0
ans : a
Q1. Differentiate twice to get the expression for acceleration as A= 9/4 t-1/2 + 3/2 t-5/2. According to the options, none of these is correct.
Q2. Force = Rate of change of momentum = Volume flowing per unit time X density X velocity
and volume flowing per unit time = area of pipe X velocity of water.
so force is propotional to Volume flowing2.
so on doubling the rate of flow, force becomes 4 times.
I can not get your Q3.
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