# 1) A body is moving along a horizontal circular path with constant speed v. What is the change in its velocity when it describes an angle?{answer should come 2v sin}2) Particle A of mass M is revolving along a circle of radius R. Particle B of mass m is revolving in another circle of radius r. If they take the same time to complete one revolution, then the ratio of their angular velocities is{answer should come 1}3) Two particles of masses M an m revolve in circular orbits of radii R and r. If the time periods of both the particles are equal, then the ratio of their linear speed is{answer should come }4) The angular velocity of a wheel increases from 600 revolutions/minute to 2400 revolutions/minute in 10 seconds. The number of revolutions made during this time interval is{answer should come 250 revolutions}5) A particle moves along a circle of radius 10 cm. If its linear speed changes from 4 m/s to 5 m/s in 1 second, then its angular acceleration will be{answer should come 10}

1
by jafiya

2014-09-28T03:38:41+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
1.  refer to diagram.

Change in velocity ΔV = V₂ - V₁ vector subtraction.
V1 and V2 are of same magnitude V but are inclined at angle Ф.  The triangle formed by the three vectors is an Isosceles triangle. Draw a perpendicular bisector on to the vector V2 - V1. The angle is bisected.

Now magnitude of V2 - V1 = 2 * sin Ф/2 * hypotenuse = 2 V sin Ф/2

3.   Let the time period of revolution of both masses be T.
In time T, m travels a distance = 2 π r and M moves a distance 2 π R.
So linear speed of m = 2π r / T           linear speed of M = 2 π R / T
Ratio = R/r

2.  Let the time period of revolution of both masses be T.   In time T mass m covers an angle of 2 π radians and M also covers an angle of 2π rad.
angular speed = ω = 2π/T = same for both

4. Revolutions made = angle Ф rotated through in 10 seconds / 2π
Ф = time duration * average angular speed = 10 * (ω₂ + ω₁) / 2
= 10 * [ (2400 + 600)/2 ] * (2π/60) rad
n = revolutions = 500π/2π = 250

5. linear speed = v = r ω
angular speed ω = v / r

angular velocities ω2 = 5 /0.1 = 50 rad/sec    ω1=4/0.1 = 40 rad/sec
angular acceleration = α = ω2 - ω1 / time = (50-40) / 1sec = 10 rad/sec²

murty sir?i have a question for you...if you dont mind...can i ask?
message me on profile
thanks n u r welcom