# data[].attributes.body
v=710⋅9.81⋅2.10​​=7205.41​​=29.344​≈5.42m/s

v≈5.42m/s​

This is the linear speed of the center of mass of the sphere as it leaves the incline

# data[].attributes.body
Q1- 4fr, 2fr , fr/2 , fr/4

(b) d<c<b<a

Q2- Solid sphere → Solid cylinder → Hollow cylinder

# data[].attributes.body
Q1 . 4FR , 2FR , FR/2 , FR/4 - part b - d<c<b<a

Q2 . Solid sphere → Solid cylinder → Hollow cylinder

# data[].attributes.body
Torque due to Force F1​: 10.4N\cdotpm

Torque due to Force F2: 32.0N\cdotpm

Torque due to Force F3: 0N\cdotpm

# data[].attributes.body
Q1- 4fr, 2fr, fr/2, fr/4

b- d<c<b>a

Q2- solid sphere solid cylinder hollow cylinder

# data[].attributes.body
Q1.

a. Torque

A=4FR , B=2FR , C=FR/2 , D=FR/4

b. D<C<B<A

Q2.

Solid sphere - Solid cylinder - Hollow cylinder

# data[].attributes.body
A- 4Fr,2fr,fr/2,fr/4

B- d<c<b<a

Solid sphere → Solid cylinder → Hollow cylinder

# data[].attributes.body
Torque due to F1=20.0 NF1​=20.0N

r=0.60m

τ1​=0.60⋅20⋅sin(150∘)=0.60⋅20⋅0.5=6.0N Counterclockwise

Torque due to F2=40.0 NF2​=40.0N

r=0.80m

τ2​=0.80⋅40⋅sin(90∘)=0.80⋅40⋅1=32.0N/m

Clockwise

Torque due to F3=50.0 NF3​=50.0N/m

r=1.0m

τ3​=1.0⋅50⋅sin(45∘)=50⋅0.7071≈35.36NClockwise

b. Net Torque about point O

τnet​=+6.0−32.0−35.36=−61.36N/m

Net Torque = −61.36 N\cdotpm−61.36N

# data[].attributes.body
Given:

Mass m=5.15 kgm=5.15kg

Radius R=0.340 mR=0.340m

Height h=2.10 mh=2.10m

Gravitational acceleration g=9.8 m/s2g=9.8m/s2

Solid sphere moment of inertia:

I=25mR2I=52​mR2

The linear speed of the center of mass is approximately:

5.42 m/s

# data[].attributes.body
F1​=20.0N, angle = 30°, lever arm = 0.60 m

F2=40.0 NF_2 = 40.0 \, \text{N}F2​=40.0N, angle = 90° (since not stated, but usually vertical), lever arm = 1.0 m

F3=50.0 NF_3 = 50.0 \, \text{N}F3​=50.0N, angle = 45°, lever arm = 0.80 m

F1​=+6.0 N.m Counterclockwise

F2=−40.0N.m Clockwise

F3= +28.3N.m Counterclockwise

# data[].attributes.body
τ1​=0.60×20.0×sin(90+30)=10.392N⋅m

τ2​=0.80×40.0×sin(90)=32.0N⋅m

τ3​=0

# data[].attributes.body
v=5.42m/s

# data[].attributes.body
1) a: 4FR, 2FR, FR/2, FR/4

b: d<c<b<a

2) solid sphere - solid cylinder - hollow cylinder

# data[].attributes.body
Q1 4fr, 2fr, fr/2, fr/4

b d<c<b<a

Q2 solid sphere → solid cylinder → hollow cylinder

# data[].attributes.body
a- Tnet=-3.55

b- Clockwise

# data[].attributes.body
A. Tnet=-3.55 Nm

B. The wheel rotates clockwise.