Question

A roller is concreted by joining together two cones at their vertices O. It is then put on two rails AB and CD that are placed asymmetrically, with its axis right angle to CD and its midpoint OF. Line joining AB and CD at the centre. It is then pushed lightly so that it begins rolling with its centre O moving parallel to CD. As it moves, the roller will bend to.

A. go straight
B. turn right
C. turn left
D. turn right than left one by one

Answer 1

Hint - This question brings us to our basic concept of trigonometry and physics. In this problem we are going to study about net force and the concept behind it. And then, with our knowledge and the information given, we will be approaching our answer.

Step-By-Step answer:
Force: It has both magnitude and direction which proves the fact that it is a vector quantity. Force is any interplay that, if we stop, brings differences in the motion and shape of the particle. It can be a push or pull. Its SI unit is Newton (N).

The picture which you can see here is the front side of the roller. The rails intersect the plane of the paper on both sides where normal reactions occur. Initially the point O is moving parallelly in the same direction as of CD which is shown by the velocity arrow.

So,
 $N_1\cos \theta \times r_1=N_2\cos \theta \times r_2$
Therefore, $N_1{r}_1=N_2{r}_2$

Now we all know that roller is rolling in forward direction

As the roller moves forward, the distance from the centre line that is $r_1$ ​turns smaller.

So, $N_1$, that is, the force will start becoming more. Hence, which implies that normal reaction $N_1>N_2$
Now by applying simple concepts we can come to a conclusion that normal reaction applied towards the horizontal direction comes
$N_1\sin \theta -N_2\sin \theta =\left(N_1-N_2\right)$ the direction of $\sin \theta$ is towards the left direction.
Now as we above have proved that $N_1>N_2$

Since, $N_1>N_2$ net force is towards the left and hence the roller moves towards the left.
This means option C is proved as the result.
Hence, the correct option is C – turn left


Note - Rotational motion happens if all particles in the substance (any object which is moving) moves in a circle about a single line. The line about which a rotation is performed is called the axis of rotation. All the radius vectors from the axis to all particles undergo the same angular displacement at the same time. The axis of rotation does not always go from between the body.