(Solved): (a) A hydraulic lift at an automobile garage consists of two oil-filled cylindrical pipes with diff ...

(a) A hydraulic lift at an automobile garage consists of two oil-filled cylindrical pipes with different diameters. A worker pushes down on the piston at one end, raising the car on the platform at the other end, as depicted in Figure B6. To handle a full range of jobs, the lift must be able to lift up cars up to \( 3000 \mathrm{~kg} \), plus the \( 400 \mathrm{~kg} \) platform on which they are parked. To avoid injury to workers, the maximum amount of force a worker needs to exert is \( 120 \mathrm{~N} \). Figure \( \mathrm{B} 6 \) i) Calculate the required diameter of the pipe, \( d \) under the platform. [3] ii) If the worker pushes down with a stroke \( 50 \mathrm{~cm} \) long, by how much will he raise the car at the other end? [2] Din used a bobber which is a sphere of radius \( 2.0 \mathrm{~cm} \) to catch fish in a river. While fishing, the bobber floats with \( 2 / 5 \) of its volume below the water, Figure B7. Initially, the fishing lines are slack, and make no forces on the bobber. The weight of the hook, line and bait is negligible. [ Use density of river water, \( \rho=1000 \mathrm{~kg} / \mathrm{m}^{3} \) ] Figure B7 i) Calculate the buoyant force acting on the bobber. [2] ii) A fish bites and pulls the bobber completely under water. What is the minimum downward force applied by the fish on the bobber? [3]