<\/span><\/h3>\n\n\n\nThe correct representation of displacement \ud835\udc51d<\/em> with time \ud835\udc61t<\/em> for a particle falling freely under gravity from rest is shown in graph (a). According to the equation of motion, \ud835\udc51=\ud835\udc62\ud835\udc61+1\/2(\ud835\udc54\ud835\udc612<\/sup><\/sub>), where \ud835\udc51 is displacement, \ud835\udc62 is initial velocity, \ud835\udc61 is time, and \ud835\udc54 is acceleration due to gravity. Given that \ud835\udc62=0, the equation simplifies to \ud835\udc51=1\/2(\ud835\udc54\ud835\udc612<\/sup>), which is equivalent to a parabolic equation \ud835\udc66=\ud835\udc4e\ud835\udc652<\/sup>. Graphs (b), (c), and (d) are incorrect as they depict linear relationships, indicating displacement decreasing with time.<\/p>\n\n\n\n<\/span>Q3. Distance-time graph in respect of a race among four persons is shown in the given figure. Consider the following statements in this regard (1996)<\/strong><\/span><\/h2>\n\n\n\n1. A stood first in the race<\/p>\n\n\n\n
2. C leads all the way<\/p>\n\n\n\n
3. Dran faster than others in the later part of the race<\/p>\n\n\n\n
Of these statements<\/em><\/p>\n\n\n\n(a) 1 and 3 are false and 2 is true<\/p>\n\n\n\n
(b) 1 and 2 are false and 3 is true<\/p>\n\n\n\n
(c) 1 and 3 are true and 2 is false<\/p>\n\n\n\n
(d) 1 is true and 2 and 3 are false<\/p>\n\n\n\n
<\/span>Ans. (b)<\/strong><\/span><\/h3>\n\n\n\nIn the context of the distance-time graph provided for a race among four persons, statements (1) and (2) are false, while (3) is true. Analyzing the graph, A, B, C, and D represent the participants, with distance plotted along the X-axis and time along the Y-axis. D took the minimum time for the same distance covered, indicating D ran faster than others in the later part of the race or secured the first position. C, on the other hand, took the maximum time, implying C was the slowest. Thus, no participant led all the way. Therefore, option (b) is correct.<\/p>\n\n\n\n
<\/span>Q4. A simple machine helps a person in doing (1996)<\/strong><\/span><\/h2>\n\n\n\n(a) less work<\/p>\n\n\n\n
(b) the same amount of work with lesser force<\/p>\n\n\n\n
(c) the same amount of work slowly<\/p>\n\n\n\n
(d) the same amount of work much faster<\/p>\n\n\n\n
<\/span>Ans. (b)<\/strong><\/span><\/h3>\n\n\n\nA simple machine is a mechanical tool that assists individuals in accomplishing tasks with less force while maintaining the same amount of work. For instance, utilizing a pulley enables us to raise heavier weights by exerting minimal force.<\/p>\n\n\n\n
<\/span>Q5. When an air bubble at the bottom of lake rises to the top, it will (1996)<\/strong><\/span><\/h2>\n\n\n\n(a) increase in size<\/p>\n\n\n\n
(b) decrease in size<\/p>\n\n\n\n
(c) maintain its size<\/p>\n\n\n\n
(d) flatten into a dish like shape<\/p>\n\n\n\n
<\/span>Ans. (a)<\/strong><\/span><\/h3>\n\n\n\nWhen an air bubble situated at the lake’s bottom ascends to the surface, its size expands. This phenomenon occurs because the pressure of the liquid escalates with depth, while the air pressure within the bubble remains equivalent to the pressure of the surrounding liquid at any given depth. Consequently, as the bubble ascends, the liquid pressure diminishes, causing an increase in pressure inside the bubble. Consequently, the volume of the bubble enlarges, leading to its expansion.<\/p>\n\n\n\n
<\/span>Q6. A liquid is flowing in a streamlined manner through a cylindrical pipe. Along a section containing the axis of the pipe, the flow profile will be not similar and will look like (1996)<\/strong><\/span><\/h2>\n\n\n\n<\/span>Ans. (d)<\/strong><\/span><\/h3>\n\n\n\nWithin a segment containing the pipe’s axis, the flow pattern will exhibit dissimilarity and resemble the depiction provided in option (d). Streamline flow characterizes the movement of a liquid where each particle passing through a point follows an identical trajectory and velocity as the preceding particle traversing the same point. In a cylindrical pipe, the liquid’s velocity peaks at the center and gradually diminishes towards the walls. Conversely, the illustrations presented in options (a), (b), and (c) are inaccurate, depicting respectively static liquid, diverse layers flowing in varying directions, and disparate layers adhering to different patterns.<\/p>\n\n\n\n
<\/span>Q7. Which one of the following is a vector quantity? (1997)<\/strong><\/span><\/h2>\n\n\n\n(a) Momentum<\/p>\n\n\n\n
(b) Pressure<\/p>\n\n\n\n
(c) Energy<\/p>\n\n\n\n
(d) Work<\/p>\n\n\n\n
<\/span>Ans. (a)<\/strong><\/span><\/h3>\n\n\n\nIn a section containing the axis of the pipe, the flow pattern will differ and resemble the depiction given in option (d). Streamline flow describes the motion of a liquid where every particle passing through a point follows the same path and speed as the preceding particle at that point. Inside a cylindrical pipe, the liquid’s velocity is highest at the center and decreases progressively towards the walls. However, the diagrams in options (a), (b), and (c) are incorrect, showing a stationary liquid, layers flowing in different directions, and layers following various patterns, respectively.<\/p>\n\n\n\n
<\/span>Q8. A smooth inclined at an angle \u03b8 with the horizontal shown in the figure. A body starts from rest and slide down the inclined surface. The time taken by the body to reach the bottom is (1997)<\/strong><\/span><\/h2>\n\n\n\n<\/span>Ans. (c)<\/strong><\/span><\/h3>\n\n\n\nA body starts from rest and slides down the inclined surface. The time taken by the body to reach the bottom is <\/p>\n\n\n\nA smooth inclined plane in the given figure is at an angle \u03b8 with the horizontal. As the body is at rest its initial velocity u = 0. Now as the body slides down the inclined surface, the acceleration due to gravity g <\/em>will be resolved into two components (as shown below) as g<\/em>sin\u03b8 and g<\/em>cos\u03b8. Now, a = g<\/em>sin\u03b8 is responsible for the body to slide down the inclined plane. Now, using the equation motion,<\/p>\n\n\n\n