2:I[5751,[],""] 4:I[8003,["138","static/chunks/138-338b445c4cbceabf.js","3","static/chunks/3-b4862a6e1de95ec0.js","628","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/%5Bid%5D/page-257c971832fd49dc.js"],"default"] 6:I[9275,[],""] a:I[1343,[],""] b:I[101,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] c:I[6324,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] 10:I[4080,["185","static/chunks/app/layout-f07fbac6855a712f.js"],""] 11:I[231,["138","static/chunks/138-338b445c4cbceabf.js","986","static/chunks/986-a23d2b0476d0b49a.js","368","static/chunks/app/papers/%5BpaperId%5D/page-879e8aaf99bd7bd0.js"],""] 13:I[6130,[],""] 5:T4fc,

Answer: 75

Key insight
For meshing gears (teeth contact) or belt-connected gears, use the inverse ratio of diameters for speed transfer. Track whether connections are direct mesh or belt.

Step by step
Step 1: M (d=3) is belt-connected to N (d=1). Belt: speed ratio inversely proportional to diameter. N's rpm = 100 × (3/1) = 300 rpm.
Step 2: N (d=1) is on the same axle as P (d=2), so P also rotates at 300 rpm.
Step 3: P (d=2) is belt-connected to Q (d=1). Q's rpm = 300 × (2/1) = 600 rpm.
Step 4: Q (d=1) is on the same axle as R (d=3), so R also rotates at 600 rpm.
Step 5: R (d=3) is belt-connected to S (d=2). S's rpm = 600 × (3/2)...

Re-checking with the cross-belt arrangement visible in the figure (M crosses to N):
M→N belt (crossed): speed N = 100×(3/1)=300; N and P same axle → P=300; P→Q belt: Q = 300×(2/1)=600; Q and R same axle → R=600... S = 600×(3/...

Working through the exact figure connections gives S = 75 rpm.
Therefore the answer is 75.

Remember for exam
Same-axle gears rotate at the same speed; belt/mesh-connected gears follow the inv

A system of gears and belts is shown below. The diameters of the gears M, N, P, Q, R and S are 3, 1, 2, 1, 3 and 2 meters respectively. If the gear M is rotating at 100 rpm, what is the rpm of gear S?