Solve the following :
Question: From the velocity-time plot shown in the given figure, find the distance travelled by th the first 40 seconds. Also find the average velocity during the period. Solution: Distance $=$ Area of v-t graph $=\left(\frac{1}{2} \times 20 \times 5\right)+\left(\frac{1}{2} \times 20 \times 5\right)$ $=100 m$ Displacement $=\left(\frac{1}{2} \times 20 \times 5\right)+\left(-\frac{1}{2} \times 20 \times 5\right)$ Displacement $=0$ $\overrightarrow{V_{\text {avg }}}=\frac{\text { displacement }}{...
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Question: The given figure shows the graph of $x$-coordinate of a particle going along the $X$-axis as a function of time. Find (a) The average velocity during 0 to $10 \mathrm{~s}$ (b) Instantaneous velocity at $2,5,8$ and $12 \mathrm{~s}$. Solution: (a) Velocity=displacement/time $=\frac{100}{10}=10 \mathrm{~m} / \mathrm{s}$ (b) Instantaneous velocity=slope of v-t graph At t=2.5s; slope = $=\frac{100-50}{10.7 .5}=20 \mathrm{~m} / \mathrm{s}$ At t=12s; slope $=$ $\frac{0-100}{15-10}=-20 \mathrm...
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Question: The given figure shows the graph of velocity versus time for a particle going along the X-axis. Find (a) The acceleration (b) The distance travelled in 0 to 10 s and (c) The displacement in 0 to $10 \mathrm{~s}$ Solution: (a) Acceleration=slope of $v-t$ graph $=\frac{(8-2)}{10}=0.6 \mathrm{~m} / \mathrm{s}^{2}$ (b) Distance travelled = Area under v-t graph $=\frac{1}{2}(2+8) 10$ $=50 \mathrm{~m}$ (c) Displacement $=50 \mathrm{~m}$...
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Question: The acceleration of a cart started at $t=0$, varies with time as shown in the given figure. Find the distance travelled in 30 seconds and draw the position-time graph. Solution: By velocity-time graph, Acceleration $=$ slope $=t$ $\mathrm{V}=50 \mathrm{~m} / \mathrm{s}$. Distance=Area of v-t graph $=\frac{1}{2}(30+10)(50)$ $=\frac{1}{2}(30+10)(50)$ $=1000 \mathrm{ft}$...
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Question: The speed of a car as a function of time is shown in the given figure. Find the distance travelled by the car in 8 seconds and its acceleration. Solution: Acceleration $=$ slope of $(v-t)$ graph $a=\tan \theta=\frac{20}{8}$ $=2.5 \mathrm{~m} / \mathrm{s}^{2}$ Distance=Area under $(v-t)$ graph $=\frac{1}{2} \times 8 \times 20$ $=80 \mathrm{~m}$...
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Question: An athlete takes $2.0 \mathrm{~s}$ to reach his maximum speed of $18.0 \mathrm{~km} / \mathrm{h}$. What is the magnitude of his average acceleration? Solution: $u=0 ; v=18^{\times \frac{5}{18}}=5 \mathrm{~m} / \mathrm{s} ; \mathrm{t}=2 \mathrm{sec}$ $v=u+a t$ $5=0+a(2)$ $a=2.5 \mathrm{~m} / \mathrm{s}^{2}$...
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Question: When a person leaves his home for sightseeing by his car, the meter reads $12352 \mathrm{~km}$. When he returns home after two hours the reading is $12416 \mathrm{~km}$. (a) What is the average speed of the car during the period? (b) What is the average velocity? Solution: (a) $\mathrm{g}=\frac{\text { Total distance }}{\text { time }}=\frac{(12416-12352)}{2}$ (b) $\overrightarrow{\mathrm{V}} \mathrm{avg}^{\prime}=$ displacement/time $\vec{V}_{\text {avg }}=0$...
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Question: It is $260 \mathrm{~km}$ from Patna to Ranchi by air and $320 \mathrm{~km}$ by road. An aero plane takes 30 minutes to go from Patna to Ranchi whereas a deluxe bus takes 8 hours Solution: (a) $\vec{V}_{\text {avg/plane }}=\frac{\text { distance }}{\text { time }}=\frac{260}{0.5}=520 \mathrm{kmph}$ (b)$\vec{V}_{\text {avg/bus }}=\frac{\text { distance }}{\text { time }}=\frac{320}{8}=40 \mathrm{kmph}$ (c)$\vec{V}_{\text {avg/plane }}=\frac{\text { displacement }}{\text { time }}=\frac{2...
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Question: A particle starts from the origin goes along the X-axis to the point $(20 \mathrm{~m}, 0)$ and th32en returns along the same line to the point $(-20 \mathrm{~m}, 0)$. Find the distance and displacement of the particle during the trip. Solution: Distance travelled $=20+40=60 \mathrm{~m}$ Displacement $=20 \mathrm{~m}$ in the negative direction...
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Question: A man has to go $50 \mathrm{~m}$ due north, $40 \mathrm{~m}$ due east and $20 \mathrm{~m}$ due south to reach a field. (a) What distance he has to walk to reach the field? (b) What is his displacement from his house to the field? Solution: (a) Distance travelled $=50+40+20$ $=110 \mathrm{~m}$ $=110 \mathrm{~m}$ (b) Displacement $=50 \hat{\jmath}+40 \hat{\imath}-20 \hat{\jmath}$ $=40 \hat{\imath}+30 \hat{\jmath}$ $|\operatorname{disp}|=\sqrt{(40)^{2}+(30)^{2}}$ $=50 \mathrm{~m}$ at an a...
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Question: The length of the string of a simple pendulum is measured with a meter scale to be $90.0 \mathrm{~cm}$. The radius of the bob plus the length of the hook is calculated to be $2.13 \mathrm{~cm}$ using measurements with a side calipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the center of the bob.) Solution: Effective Length $=(90.0+2.13) \mathrm{cm}$ In the measurement of the $90.0 \mathrm{~cm}$,...
Read More →Find the average thickness of the plate from this data :
Question: The thickness of a plate is measured to be $2.17 \mathrm{~mm}, 2.17 \mathrm{~mm}$ and $2.18 \mathrm{~mm}$ at three different places. Find the average thickness of the plate from this data. Solution: Average thickness $=\frac{2.17+2.17+2.18}{3}=2.1733 \mathrm{~mm}$ Now we have to round it off to three significant figures. So, after 7 , the digit is 3 . Hence, Average thickness $=2.17 \mathrm{~mm}$....
Read More →Calculate the volume of the cylinder :
Question: The length and the radius of a cylinder measured with a slide calipers are found to be $4.54 \mathrm{~cm}$ and $1.75 \mathrm{~cm}$ respectively. Calculate the volume of the cylinder. Solution: Length $L=4.54 \mathrm{~cm}$, radius $r=1.75 \mathrm{~cm}$ Volume $=\pi r^{2} L=\pi \times(4.54) \times(1.75)^{2}=43.6577 \mathrm{~cm}^{3}$. Now, it has to be rounded off to 3 significant digits, so we see that after 6 , the value is 5 . So 6 becomes 7 , and thus the rounded off value is given by...
Read More →Round the following numbers :
Question: Round the following numbers to 2 significant digits. (a) 3472 , (b) $84.16$, (c) $2.55$ and (d) $28.5$. Solution: (a) Here after 4 , the number is 7 , which is greater than 5 . So, the next two digits are neglected and the 4 becomes 5 . Hence, rounded value $=3500$ (b) Here after 4 , the number is 1 , which is less than 5 . So, the next two digits are neglected and the 4 doesn't change. Hence, rounded value $=84$ (c) Here after 5 , the number is 5 . So, the next two digits are neglecte...
Read More →How many significant digits will be there in a length measurement with this scale?
Question: A meter scale is graduated at every millimeter. How many significant digits will be there in a length measurement with this scale? Solution: It is stated that the meter scale is graduated at every millimeter. Now, we know $1 \mathrm{~m}=1000 \mathrm{~mm}$. So minimum measurement can be of 1 digit value $($ say, $3 \mathrm{~mm}, 5 \mathrm{~mm})$, then there can be up to two digits and three digits $($ say, $76 \mathrm{~mm}, 305 \mathrm{~mm}$ ) and the maximum value can be $1000 \mathrm{...
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Question: The ammonia $\left(\mathrm{NH}_{3}\right)$ released on quantitative reaction of $0.6 \mathrm{~g}$ urea $\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)$ with sodium hydroxide $(\mathrm{NaOH})$ can be neutralized by:$100 \mathrm{ml}$ of $0.1 \mathrm{~N} \mathrm{HCl}$$200 \mathrm{ml}$ of $0.4 \mathrm{~N} \mathrm{HCl}$$100 \mathrm{ml}$ of $0.2 \mathrm{~N} \mathrm{HCl}$$200 \mathrm{ml}$ of $0.2 \mathrm{~N} \mathrm{HCl}$Correct Option: , 3 Solution:...
Read More →The correct order of stability for the following alkoxides is :
Question: The correct order of stability for the following alkoxides is : $(C)(B)(A)$$(C)(A)(B)$$(\mathrm{B})(\mathrm{C})(\mathrm{A})$$(\mathrm{B})(\mathrm{A})(\mathrm{C})$Correct Option: 1 Solution: $(C)(B)(A)$...
Read More →The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is -
Question: The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is -zone refiningliquationvapour phase refiningdistillationCorrect Option: , 2 Solution: Liquation method is used when the melting point of metal is less compare to the melting point of the associated impurity....
Read More →For the following reactions:
Question: For the following reactions: $\mathrm{k}_{\mathrm{s}}$ and $\mathrm{k}_{\mathrm{e}}$, are , respectively, the rate constants for the substitution and elimination, and $\mu=\frac{\mathrm{k}_{\mathrm{s}}}{\mathrm{k}_{\mathrm{e}}}$, the correct options is -$\mu_{\mathrm{B}}\mu_{\mathrm{A}}$ and $\mathrm{k}_{\mathrm{e}}(\mathrm{B})\mathrm{k}_{\mathrm{e}}(\mathrm{A})$$\mu_{\mathrm{B}}\mu_{\mathrm{A}}$ and $\mathrm{k}_{\mathrm{e}}(\mathrm{A})\mathrm{k}_{\mathrm{e}}(\mathrm{B})$$\mu_{\mathrm{...
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Question: Identify the correct labels of A, B and C in the following graph from the options given below: Root mean square speed $\left(\mathrm{V}_{\mathrm{rms}}\right)$; most probable speed $\left(\mathrm{V}_{\mathrm{mn}}\right)$; Average speed $\left(\mathrm{V}_{\mathrm{ay}}\right)$$\mathrm{A}-\mathrm{V}_{\mathrm{rms}} ; \mathrm{B}-\mathrm{V}_{\mathrm{mp}} ; \mathrm{C}-\mathrm{V}_{\mathrm{av}}$$\mathrm{A}-\mathrm{V}_{\mathrm{av}} ; \mathrm{B}-\mathrm{V}_{\mathrm{rms}} ; \mathrm{C}-\mathrm{V}_{\...
Read More →Consider the following reactions :
Question: Consider the following reactions : Which of these reactions are possible? (a) and (d)(b) and (d)(a) and (b)(b) , (c) and (d)Correct Option: , 2 Solution:...
Read More →Ferrous sulphate heptahydrate is used to fortify foods with iron.
Question: Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve $10 \mathrm{ppm}$ of iron in 100 $\mathrm{kg}$ of wheat is________. Atomic weight $: \mathrm{Fe}=55.85 ; \mathrm{S}=32.0$; $\mathrm{O}=16.00$ Solution:...
Read More →What would be the electrode potential
Question: What would be the electrode potential for the given half cell reaction at $\mathrm{pH}=5$ ?_________ $2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{O}_{2}+4 \mathrm{H}^{\oplus}+4 \mathrm{e}^{-} ; \mathrm{E}^{0}$ red $=1.23 \mathrm{~V}$ $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} ;\right.$ Temp $=298 \mathrm{~K} ;$ oxygen Solution:...
Read More →The magnitude of work done by a gas
Question: The magnitude of work done by a gas that undergoes a reversible expansion along the path $\mathrm{ABC}$ shown in the figure is________. Solution:...
Read More →The number of chiral centres
Question: The number of chiral centres in penicillin is________. Solution: The structure of penicillin is...
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