Question

A massive cylinder rolls without sliding up an inclined plane with an angle of 30º. The cylinder's radius is 3.14cm and the mass is 2.71kg. What are gravity (G), normal force (N) and friction force (R) on the cylinder?

• G=23N, N=23N, R=3,8N
• G=27N, N=23N, R=3,8N
• G=27N, N=23N, R=5,3N
• G=23N, N=23N, R=4,4N
• G=27N, N=27N, R=4,4N
• G=27N, N=27N, R=5,3N
• G=23N, N=23N, R=5,3N
• G=27N, N=27N, R=3,8N
• G=27N, N=23N, R=4,4N

A carousel has the shape of a circular disc with radius 0.9m and mass 40kg. The carousel rotates at 2 revolutions per second. A child cups on the carousel at the very edge. The carousel and children then rotate at 1 rpm. What is the child's mass?

• 13kg
• 36kg
• 20kg
• 44kg
• 40kg
• 30kg

A two-atomic ideal gas has the starting pressure p0, the starting volume V0 and the starting temperature 0ºC. The gas undergoes an isobar compression so that the new volume becomes V09. What is the new print?

p09

• 0,9•p₀
• 9p₀
• p₀
• (p0)9
• impossible to answere

Answer 1

a). First consider the following FBD + Diagram of the given situation;

Now, from FBD let's write down the Newton's 2nd Law of Motion in X & Y - Direction separately;

Now, again apply the Newton's 2nd law of motion for rotation of the cylinder;

But,

So, from the first relationship, we get -

​​​​​​and from above relations and FBD, we have the Normal Force as ;

and

b). For this problem we will also use Newton's 2nd law of motion but in terms of angular momentum conservation principle i.e., when there is no external force is applied, momentum is conserved;

So, Now, you can find the value for 'm', i.e., mass of the child put on the edge.

d). Please elaborate clearly so that I can answer the problem. Thank you.

Note:- Time was limited so I could not write the final answer for the second problem (b). But the concept is true as I have already mentioned.