A $2kW$ internal combustion engine drives a sprocket at $1200rpm.$ The driven element has to rotate at about $480rpm,$ where moderate shocks are expected.

a$.$ Find the number of teeth at driver and driven sprockets

b$.$ Find the pitch of the simplex chain required.

c$.$ What is the recommended lubrication type?

d$.$ What is the chain length, if the centers of the driver and driven sprockets are $0\mathrm{.}50m$ apart?