1)A disk and a hoop of the same mass and radius are released at the same time at

Question

1)A disk and a hoop of the same mass and radius are released at the same time at the top of an plane and roll without slipping. Which object reaches the bottom of the incline first? B) The dishk C) Both reach the bottom at the same time D) It depends on the angle of inclination. E) It depends on the length of the inclined surface. 2) A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan? A) 0.86 rad/s2 B) 0.74 rad/s2 C) 0.37 rad/s2 D) 11.6 rad/s2 E) 1.16 rad/s2 3) A two-dimensional object placed in the xy-plane has three forces acting on it: a force of 3.0 N along the x-axis acting at a point (3 m, 4 m); A force of 2.0 N along the y-axis acting at (62 m, 5 m); and a force of 5 N in the negative x direction acting at (-2 m, -3 m). What is the net torque about the point (1 m, 1 m)? A) 7 N m counterclockwise B) 23 N m clockwise C) 3 N m counterclockwise D) 31 N m clockwise E) 7 N m clockwise on pushes on a doorknob with a force of 5.00 N. The direction of the force is at an angle of b is located 0.800 m from axis of the door. The d from the perpendicular to the surface of inges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s2. What is the moment of inertia of the door about the hinges? A) 4.28 kg-m2 B) 7.52 kg m2 C) 1.88 kg-m2 D) 0.684 kg-m2 E) 2.74 kg-m2 5) An object is rotating with an angular momentum of magnitude 20.0 kgm2/s in a direction directly east. A torque of magnitude 10.0 N-m acts in a direction 30° north of east acts on the object for 5.00 s. What is the angular momentum after the torque has acted? A) 45.0 kg m2/s, 51.3° north of east B) 68.1 kg-m2/s, 21.5° north of east C) 25.0 kg m2/s, 51.3° north of east D) 63.3 kg-m2/s east E) 32.0 kg-m2/s, 51.3° north of east 6) A 3.00-m long plank of negligible mass has a 30.0-kg mass at one end and a 40.0-kg mass at the other end. How far from the 30.0-kg mass should a fulcrum be placed so that the plank is balanced? A) 1.71 m B) 1.29 m C) 0.750 m D) 1.50 m 7) A cable is 100-m long and has a cross-sectional area of 1 mm2. A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 x 1011 N/m2. How far does it stretch? A) 0.001m'he B) 0.01 m C) 0.10 m D) 1.0 m

Explanation / Answer

Apply conservation of energy

m gh = 1/2 mv^2 + 1/2 I w^2

since there is no slipping th e angualr velocity w = v/r

for dsik I = mr^2/2

mgh = 1/2 m v^2 + 1/2 ( mr^2/2) ( v/r)^2

g h = 1/2 v^2 + 1/4 v^2

v = sqrt(4 g h/3)

= 1.15 sqrt gh ------------(1)

for disk

I = mr^2

mgh = 1/2 m v^2 + 1/2 ( mr^2) ( v/r)^2

gh = 1/2 v^2 + 1/2 v^2
v= sqrt(gh) ---------(2)

from the equation (1) and (2) it is clear that dsik reaches bottom first

option (B) is correct answer

As per chegg guide lines I did first question kindly post remaining questions in the next post

(2)

from the rotational kinematic equation

alpha = wf- wo/ t = 6.3-10/5 = -0.74 rad/s^2

magnitude = 0.74 rad/s^2

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