Question

The figure shows a mechanical set-up. The mechanism can be suitably described as:
                         

(A) conversion of the rotational motion of crank into linear motion of slider
(B) conversion of linear motion of slider into rotational motion of crank
(C) conversion of the rotational motion of slider into linear motion of crank
(D) conversion of linear motion of crank into rotational motion of slider

Answer 1

Hint: In the above diagram, the crank is fixed about an axis. This crank is attached to an arm which extends up to the slider, that is, both the crank and the slider are connected through this common arm. This means that if one of them is given a certain velocity or acceleration, the other one is also affected. We shall use this analogy to proceed ahead in our solution.

Complete step-by-step answer:
We will make two separate cases for this problem.
Case (1): When the crank is moving initially:
In this case, the crank is moving, that is, it is performing rotational motion. This rotational motion will affect the stationary slider. Since the slider is restricted from two opposite sides, it can only move linearly from H to J and then J to H. Assuming these two points are the points of maximum displacement.
Thus, in this case, conversion of the rotational motion of the crank into linear motion of the slider takes place.
Case (2): When the slider is moving initially:
In this case, the slider is moving, that is, it is performing linear oscillatory motion. This linear motion will affect the stationary crank. Since the crank is restricted on its axis, it can only move about it in circles from A to B and then B to A continuously.
Thus, in this case, conversion of linear motion of the slider into rotational motion of crank takes place.
Since, in our problem, the crank has been given as moving, therefore it comes under case (1).
Hence, conversion of the rotational motion of the crank into linear motion of the slider takes place.

So, the correct answer is “Option A”.

Note: In these types of practical questions, one should be able to visualize the outcome or dependence of one type of motion on another. Also, the mechanism shown in the problem is the basis on which pistons inside an engine work. These pistons run the gears in the gearbox which in turn are connected to shafts that rotate the wheels.