What Are the Correct Answers to These Physics Multiple Choice Questions?

[key]

Hi can someone please help me with these multiple choice questions



A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

1. If the plane is frictionless, what is the speed vcm, of the center of mass of the sphere at the bottom of the incline?
(A) (B) (C) (D) (E)


I think the answer is A

2.. The momentum p of a moving object as a function of time t is given by the expression p = kt3, where k is a constant. The force causing this motion is given by the expression
(A) 3kt2 (B) 3kt2/2 (C) kt2/3 (D) kt4 (E) kt4/4

I think the answer is B




3. A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs?
(A) Linear momentum is converted to angular momentum.
(B) Kinetic energy is converted to angular momentum.
(C) Rotational kinetic energy is conserved.
(D) Translational kinetic energy is conserved.
(E) Linear momentum and angular momentum are both conserved.

I think the answer is E







4. Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s.

What is the magnitude of the total momentum of the two puck system after the collision?
(A) 1.0 kg•m/s (B) 3.5 kg•m/s (C) 5.0 kg•m/s (D) 7.0 kg•m/s (E) 5.5 kg•m/s

I think the answers is D



5. A mass M suspended by a spring with force constant k has a period T when set into oscillation on Earth. Its period on Mars, whose mass is about 1/9 and radius 1/2 that of Earth, is most nearly
(A) 1/3 T (B) 2/3 T (C) T (D) 3/2 T (E) 3 T

I think the answer is C.


6. A student is testing the kinematic equations for uniformly accelerated motion by measuring the time it takes for light weight plastic balls to fall to the floor from a height of 3 m in the lab. The student predicts the time to fall using g as 9.80 m/s2 but finds the measured time to be 35% greater. Which of the following is the most likely cause of the large percent error?
(A) The acceleration due to gravity is 70% greater than 9.80 m/s2 at this location.
(B) The acceleration due to gravity is 70% less than 9.80 m/s2 at this location.
(C) Air resistance increases the downward acceleration.
(D) The acceleration of the plastic balls is not uniform.
(E) The plastic balls are not truly spherical.

I think the answer is A

7. An object is thrown with velocity v from the edge of a cliff above level ground. Neglect air resistance. In order for the object to travel a maximum horizontal distance from the cliff before hitting the ground, the throw should be at an angle θ with respect to the horizontal of
(A) greater than 60° above the horizontal
(B) greater than 45° but less than 60° above the horizontal
(C) greater than zero but less than 45° above the horizontal
(D) zero
(E) greater than zero but less than 45° below the horizontal

I think the answer is D

8. The escape speed for a rocket at Earth's surface is ve . What would be the rocket's escape speed from the surface of a planet with twice Earth's mass and the same radius as Earth?
(A) 2 ve (B) (C) ve (D) (E) ve/2

I think the answer is A

 

[tiny-tim]

Hi key!

(try using the X² tag just above the Reply box )

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

1. If the plane is frictionless, what is the speed vcm, of the center of mass of the sphere at the bottom of the incline?
(A) (B) (C) (D) (E)


I think the answer is A

erm … aren't you forgetting something? :rofl: :rofl: :rofl:

2.. The momentum p of a moving object as a function of time t is given by the expression p = kt3, where k is a constant. The force causing this motion is given by the expression
(A) 3kt2 (B) 3kt2/2 (C) kt2/3 (D) kt4 (E) kt4/4

I think the answer is B

Why? Give reasons (and yes, I know the question doesn't ask for them)

3. A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs?
(A) Linear momentum is converted to angular momentum.
(B) Kinetic energy is converted to angular momentum.
(C) Rotational kinetic energy is conserved.
(D) Translational kinetic energy is conserved.
(E) Linear momentum and angular momentum are both conserved.

I think the answer is E

Yes.

4. Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s.

What is the magnitude of the total momentum of the two puck system after the collision?
(A) 1.0 kg•m/s (B) 3.5 kg•m/s (C) 5.0 kg•m/s (D) 7.0 kg•m/s (E) 5.5 kg•m/s

I think the answers is D

You've added the total momentum (3 and 4) before the collision.

How do you add momentums? Is it the same after the collision?

 

[Moetasim]

Hello, I'm happy to assist you with these multiple choice questions. Here are my answers and explanations:

1. The correct answer is A. According to the law of conservation of energy, the total energy of the system (sphere) remains constant, and is equal to the sum of its potential and kinetic energy. At the top of the incline, the sphere only has potential energy, which is converted into kinetic energy as it rolls down the incline. Therefore, the velocity of the center of mass at the bottom of the incline can be calculated using the equation: mgh = (1/2)mv^2 + (1/2)Iω^2, where m is the mass of the sphere, g is the acceleration due to gravity, h is the height of the incline, v is the velocity of the center of mass, I is the rotational inertia, and ω is the angular velocity. Since the sphere is released from rest, ω = v/r, where r is the radius of the sphere. Plugging in the given values and solving for v, we get v = √(2gh), which is option A.

2. The correct answer is B. The force causing the motion is equal to the rate of change of momentum, according to Newton's second law. Therefore, F = dp/dt = d(kt^3)/dt = 3kt^2. This is option B.

3. The correct answer is E. In this situation, both linear momentum and angular momentum are conserved. The skater adds linear momentum to the board by jumping onto it, causing it to slide and rotate. The board's linear momentum is transferred to the skater, while its angular momentum remains the same. This is because the skater's mass is much smaller than the board's, and thus has a negligible effect on its rotational inertia. Therefore, both linear and angular momentum are conserved in this situation.

4. The correct answer is D. According to the law of conservation of momentum, the total momentum of a system remains constant, regardless of any internal forces acting on it. Therefore, the total momentum of the two pucks before and after the collision must be the same. Since the 1.5 kg puck is moving east and the 4.0 kg puck is moving north, their momenta are in perpendicular directions. Using vector addition, the magnitude of the total momentum can be calculated