302 - Mechanics part 1 Questions Answers
The acceleration of a particle, varies with time according to the relation a=-mw2sinwt.The displacement of this particle at a time t will be
1) m sin(wt)
2) mwcos(wt)
3) mwsin(wt)
4) -1/2(mw2sinwt)t2
a = dv/dt = -mw2sinwt
so ∫dv = ∫-mw2sinwtdt
so v = mwcoswt + C
at t=0, v=0 so 0 = mw+C or C = -mw
so v = -mw(1-coswt)
similarly put v = ds/dt and integrate again
A motor boat going down stream ,overtakes a floating object in water .One hour later ,the motor boat turned back .If speed of motor boat in still water is constant and flow velocity is also assumed constant,motor boat will again pass the floating object after time 't ' given by
1)Greater than 2 hrs
2)Equal to 2 hrs
3)less than 2 hrs
4)less than 1 hr
see video in you tube under the name iitbrain
video i e irodov 1.1
time will be 1 hour
A paper weight is dropped from the roof of a 35 storey building each storey being 3m high. It passes the ceiling of the 20th storey at x m/s [g=10 m/s2]. Find x.
total height = (35-20+1)*3 = 48 m
now solve
A lift with open top is moving up with acceleration f. A body is thrown up with speed u relative to lift and it comes back to lift in time t. Then speed u is ...
{g = acceleration due to gravity}
relative acc. = g+f
and relative velocity = u
now solve
A projectile is thrown with speed 40 ms-1 at angle θ from horizontal. It is found that projectile as at same height at 1s and 3s. What is the angle of projection?
It is found that projectile as at same height at 1s and 3s, so half time of flight = 2 sec
now solve
A particle is thrown with a velocity of u m/s. It passes A and B at time t1 = 1s and t2 = 3s. The value of u is (g=10 m/s2).
question is not complete
When a force F acts on a particle of mass m, the acceleration of particle becomes a. Now if two forces of magnitude 3F and 4F acts on the particle (both are at an angle of 90° from mass m) simultaneously , then the acceleration of the particle is ..............
resultant force = 5F
so acceleration = 5a
A man moves in an open field such that after moving 10m on a straight line, he makes a
sharp turn of 60° to his left. Find the displacement after 8 such turns
draw a hexagon
just after 8 such turn displacement = 10√3
a particle is moving eastwards with a speed of 6m/s. After 6s, the particle is found to be moving with same speed in a direction 60° north of east. The magnitude of average acceleration in this interval of time is ..............
initial velocity = 6i
final velocity = 6cos60i+6sin60j
now solve
a body is dropped from a certain height h (h is very large) and second body is thrown downward with velocity of 5 m/s simultaneously. What will be difference in heights of the two bodies after 3s.
g is acting on both bodies so difference = 5*3 = 15 m