Q: In SI units, the dimensions of μ0ε0 is(a) A−1TML3(b) AT2M−1 L−1(c) AT−3ML3/2(d) A2 T3M−1 L−2

Dimensions of ε0 (permittivity of free space) are[ε0]=M−1 L−3 T4 A2As, c= speed of light.∴ Dimension of [c]=[LT−1]So, dimensions of μ0ε0 are[μ0ε0]=[ε0μ0ε02]=[ε0c][∵c2=μ0ε01]=[M−1 L−3 T4 A2][LT−1]=[M−1 L−2 T3 A2]

Q: Which one of the following represents the correct dimensions of the coefficient of viscosity?(a) [ML−1 T−2](b) [MLT−1](c) [ML−1 T−1](d) [ML−2 T−2]

By Newton's formula, η=A(Δvx/Δz)F∴ Dimensions of η=Dimensions of area×Dimensions of velocity gradientDimensions of force =[L2][T−1][MLT−2]=[ML−1 T−1]

Question 1

In SI units, the dimensions of μ0​ε0​​​ is(a) A−1TML3(b) AT2M−1 L−1(c) AT−3ML3/2(d) A2 T3M−1 L−2

Accepted Answer

Dimensions of ε0​ (permittivity of free space) are[ε0​]=M−1 L−3 T4 A2As, c= speed of light.∴ Dimension of [c]=[LT−1]So, dimensions of μ0​ε0​​​ are[μ0​ε0​​​]=[ε0​μ0​ε02​​​]=[ε0​c][∵c2=μ0​ε0​1​]=[M−1 L−3 T4 A2][LT−1]=[M−1 L−2 T3 A2]

Question 2

The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is(a) 37.030 cm2(b) 37.0 cm2(c) 37.03 cm2(d) 37 cm2

Accepted Answer

Area of 1 square =529 cm2Area of seven such squares =7 times addition of area of 1 square =5.29+5.29+529…7 times =37.03 cm2As we know that, if in the measured values to be added/subtracted the least number of significant digits after the decimal is n.Then, in the sum or difference also, the number of significant digits after the decimal should be n. Here, number of digits after decimal in 5.29 is 2 , so our answer also contains only two digits after decimal point.∴ Area required =37.03 cm2

Question 3

The pitch and the number of divisions, on the circular scale for a given screw gauge are 0.5 mm and 100 , respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line.The readings of the main scale and the circular scale for a thin sheet are 5.5 mm and 48 respectively, the thickness of this sheet is(a) 5.950 mm(b) 5.725 mm(c) 5.755 mm(d) 5.740 mm

Accepted Answer

For a measuring device, the least count is the smallest value that can be measured by measuring instrument. Least count =Total divisions on the scaleMinimum reading on main−scale​ Here, screw gauge is used for measurement therefore,LC=number of divisionPitch​LC=1000.5​ mmLC=5×10−3 mmAccording to question, the zero line of its circular scale lies 3 division below the mean line and the readings of main scale =5.5 mmThe reading of circular scale =48 then the actual value is given by actual value of thickness (t)=( main scale reading) + (circular scale reading + number of division below mean line) ×LC ⇒t=5.5 mm+(48+3)×5×10−3 mm ⇒t=5.755 mm

Question 4

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?(a) A meter scale(b) A vernier caliper where the 10 divisions in vernier scale matches with 9 divisions in main scale and main scale has 10 divisions in 1 cm(c) A screw gauge having 100 divisions in the circular scale and pitch as 1 mm(d) A screw gauge having 50 divisions in the circular scale and pitch as 1 mm

Accepted Answer

If student measure 3.50 cm, it means that there in an uncertainly of order 0.01 cm.For vernier scale with 1MSD=1 mm and 9MSD =10VSD∴ LC of VC=1MSD−1VSD=101​(1−109​)=1001​ cm

Question 5

The respective number of significant figures for the numbers 23.023,0.0003 and 2.1×10−3 are(a) 5,1,2(b) 5,1,5(c) 5,5,2(d) 4, 4, 2

Accepted Answer

The reliable digit plus the first uncertain digit is known as significant figures.For the number 23.023, all the non-zero digits are significant, hence 5.For the number 0.0003, number is less than 1 , the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant, hence 1.For the number 2.1×10−3, significant figures are 2 .

Question 6

The dimensions of magnetic field in M,L,T and C( coulomb ) is given as(a) [MLT−1C−1](b) [MT2C−2](c) [MT−1C−1](d) [MT2C−1]

Accepted Answer

From the relation F=qvB⇒[MLT−2]=[C][LT−1][B]⇒[B]=[MC−1 T−1]

Question 7

The 'rad' is the correct unit used to report the measurement of(a) the ability of a beam of gamma ray photons to produce ions in a target(b) the energy delivered by radiation to a target(c) the biological effect of radiation(d) the rate of decay of a radioactive source

Accepted Answer

'Rad' is used to measure biological effect of radiation.

Question 8

Out of the following pairs, which one does not have identical dimensions?(a) Angular momentum and Planck's constant(b) Impulse and momentum(c) Moment of inertia and moment of a force(d) Work and torque

Accepted Answer

Moment of inertia, I=mr2∴[I]=[ML2]and τ= Moment of force =r×F∴[τ]=[L][MLT−2]=[ML2 T−2]

Question 9

Which one of the following represents the correct dimensions of the coefficient of viscosity?(a) [ML−1 T−2](b) [MLT−1](c) [ML−1 T−1](d) [ML−2 T−2]

Accepted Answer

By Newton's formula, η=A(Δvx​/Δz)F​∴ Dimensions of η=Dimensions of area×Dimensions of velocity gradientDimensions of force​ =[L2][T−1][MLT−2]​=[ML−1 T−1]

Question 10

The physical quantities not having same dimensions are(a) torque and work(b) momentum and Planck's constant(c) stress and Young's modulus(d) speed and (μ0​ε0​)−1/2

Accepted Answer

Planck's constant (in terms of unit)
h=Js=[ML2T−2][T]=[ML2T−1]
Momentum (p)=kg ms−1
=[M][L][T−1]=[MLT−1]

Question 11

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.(a)(b)(c)(d)

Accepted Answer

If velocity versus time graph is a straight line with negative slope, then acceleration is constant and negative.
With a negative slope distance-time graph will be parabolic (s=ut−21​at2).
So, option (b) will be incorrect.

Question 12

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?(a)(b)(c)(d)

Accepted Answer

Initially velocity keeps on decreasing at a constant rate, then it increases in negative direction with same rate.

Question 13

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? Assume stones do not rebound after hitting the ground and neglect air resistance, take g=10 m/s2 )(a)(b)(c)(d)

Accepted Answer

Concept of relative motion can be applied to predict the nature of motion of one particle with respect to the other.Consider the stones thrown up simultaneously as shown in the diagram below.Considering motion of the Considering motion of the second particle with respect to the first we have relative acceleration∣a21​∣=∣a2​−a1​∣=g−g=0Thus, motion of first particle is straight line with respect to second particle till the first particle strikes ground at a time given by−240=10t−21​×10×t2or t2−2t−48=0or t2−8t+6t−48=0or t=8,−6 (not possible)Thus, distance covered by second particle with respect to first particle in 8 s iss12​=(v21​)t=(40−10)(8s)=30×8=240mSimilarly, time taken by second particle to strike the ground is given by−240=40t−21​×10×t2Or −240=40t−5t2Or 5t2−40t−240=0 t2−8t−48=0 t2−12t+4t−48=0Or t(t−12)+4(t−12)=0 or t=12,−4 (not possible) Thus, after 8 s, magnitude of relative velocity will increase upto 12 s when second particle strikes the ground.

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Solutions for Arihant Physics JEE Main Chapterwise Solutions (2019-2002)

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