Question S: (.25 p) A baseball is thrown vertically upward and feels no air resi

Question

Question S: (.25 p) A baseball is thrown vertically upward and feels no air resistance. As it is rising: A) both its momentum and its mechanical energy are conserved. B) its momentum is not conserved, but its mechanical energy is conserved. C) both its momentum and its kinetic energy are conserved. D) its kinetic energy is conserved, but its momentum is not conserved. E) its gravitational potential energy is not conserved, buts its momentum is conserved. Question (.25 pt) A merry-go-round spins freely when Janice moves quickly to the center along a radius of the memy-go-round. It is true to say that A) the moment of inertia of the system decreases and the angular speed increases, B) the moment of inertia ofthe system decreases and the angular speed decreases. C) the moment of inertia ofthe system decreases and the angular speed remains the same. D) the moment of inertia of the system increases and the angular speed increases. E) the moment of inertia of the system increases and the angular speed d Question (.25 p) As you are leaving a building, the door opens outward. Ifthe hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it? A) up C) to your left D) to your right E) forwards Question Ra (.25 p) A solid sphere mR') is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes an angle of 25.0 with the horizontal. What is the speed of the sphere after it has rolled 3.00 m up the ramp? A) 1.58 m/s B) 1.91 m/s D) 2.16 m/s E) 4.20 m/s Question 9 (1.25 p) A solid sphere (I mR solid cylinder (I- mR and a hollow pipe (I-mR2 all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top ofan inclined plane and roll without slipping, which one will reach the bottom first? A) solid sphere. B) hollow pipe. D) They all reach the bottom at the same time. E) None of the above.

Explanation / Answer

Ans 5)

B) Its momentum is not conserved but its mechanical energy is conserved

Reason:
Gravitational force is acting, hence net force non-zero. So, momentum not conserved.
But gravitation force is conservative by nature, hence mechanical energy conserved.
So option B is correct.

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Ans 6)
A) Moment of inertia of system decreases and angular speed increases

Reason: Because Janice is moving towards centre, the mass of Janice is getting closer to centre of rotation ie axis. Hence moment of inertia decreases as it depends on extent of distribution of mass wrt centre.
But net torque on system is still zero. Hence angular momentum is conserved , hence resultant angular velocuty increases so as to conserve momentum.

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Ans 7)

Ans B) Down

As we open door, V = W x R
V is in forward direction pointing forward..
R or radius is from right to left.
and cross product is involved here.
So, W or angular velocity is directed DOWN.
You can get by applying right hand thumb rule.

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Ans 7)

Applying conservation of energy:

Rotational KE = 0.5*I*w2
w = v/R

w = angular velocity
v= 4.5 m/s

Linear KE = 0.5*m*v2
= 10.125m joules

So. RKE = 0.5* 2/5 * m * v2
= 4.05m joules

Total = 10.125m + 4.05m = 14.175m joules

Sphere rolls up 3 metres.
PE = mgh
h = 3*sin25o
= 1.5

PE = m*9.8*1.26
= 12.425m joules

So, remaining energy = 14.175m - 12.425m
= 1.75m joules

1.75m = 0.5*m*vf2 *(2/5 + 1)
or vf2 = 2.5
or vf = 1.58 m/s

Ans A) 1.58 m/s

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Ans 9)

For a uniform solid sphere, the moment of inertia I=(2/5)*M*R2
For a hollow tube, I=M*R2
and for a uniform solid cylinder I=(1/2)*M*R2

And PE converted to kinetic energy.
The one with lower Moment of inertia has higher KE.
?

So, solid shpere has lowest moment of inertia.

Ans A) Solid sphere

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