Step 1: Carefully observe the arrangement of the broken plate in Figure A. It consists of six pieces, but only five are placed. The missing piece must complete the overall structure.
Step 2: Analyze the shape and design of the missing portion. The curvature and pattern on the plate must align perfectly with the given options (\( P, Q, R, S \)).
Step 3: Compare each of the given choices with the missing space. Piece \( R \) matches the missing section precisely, both in terms of design continuity and shape. 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):