33. A stone is tied to one end of a string and whirled in a horizontal circle of radius 1 m at 20 revolutions
per minute. Calculate the angular velocity and linear speed of the stone. Also find the centripetal
acceleration.
34. A force of 10 N acts for 20 second on a body of mass 2 kg initially at rest. Calculate the energy required
by the body and the work done by the applied force.
35. If the earth has a mass 9 times and radius twice of the planet mars, calculate the minimum speed
required by a rocket to pull out of the gravitational force of Mars. Escape speed for an object on the
surface of the earth is 11.2 kms-1
.
Answers
Answer:
Given length of the string l= 1 m also angular velocity ω=
44
22
revolution/second.
We know linear velocity v=ω×r
Thus velocity v=
44
22
×1=0.5 m/s
And we know centripetal or radial acceleration a
c
=
r
v
2
Thus a
c
=0.25m/s
2
2- Force = mass × acceleration
F=10N
m=2kg
then,
a=
m
F
=
2
10
=5m/s
2
(i) Now,
u=0
t=3sec
v=u+at=0+3×5=15m/s
(ii)Initialmomentum=mu=2×0=0
Finalmomentum=mv=2×15=30kg−m/s
Change in momentum=Final momentum - Initial momentum
=30−0=30kg−m/s
3- Given: Me = 9 Mm, and Re = 2 Rm, ve (escape speed on surface of Earth) = 11.2 km/s
Let Vm be the speed required to pull out of the gravitational force of mars.
We know that
and
Dividing, we get
⇒ vm = 5.3 km/s
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