Step 1: Observe the word "ARCH" in Figure B. Four circular cutouts have been made within the letters. These cutouts contain unique sections of the letters.
Step 2: Compare the cutouts from Figure B with the given options (\( P, Q, R, S \)). The correct group should exactly match the missing sections in terms of alignment, shape, and letter strokes.
Step 3: After careful observation, the group labeled \( R \) contains the four exact cutouts extracted from "ARCH". The patterns within the circles align with the letter fragments in Figure B. Thus, the correct answer is option C (\( R \)).
Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $ D $ of a tube. The measured value of $ D $ is:
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity):