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1. A student measures the distance traveled in free fall of a body, initially at rest in a given time. He uses this data to estimate \(g,\) the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are \(e_1\) and \(e_2\) respectively, the error in the estimation of \(g\) is:
1. \(e_2-e_1\)
2. \(e_1+2e_2\)
3. \(e_1+e_2\)
4. \(e_1-2e_2\)

$$

2.

Given the equation \(\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}\). The units of \(a\) will be: (where \(P\) is pressure and \(V\) is volume)
1. \(\text{dyne} \times \text{cm}^5\)
2. \(\text{dyne} \times \text{cm}^4\)
3. \(\text{dyne} / \text{cm}^3\)
4. \(\text{dyne} / \text{cm}^2\)

3.

Dimensional formula $M{L}^{-1}{T}^{-2}$ does not represent the physical quantity
1. Young's modulus of elasticity
2. Stress
3. Strain
4. Pressure

4.

Dimensional formula for volume elasticity is
1. $M^1{L}^{-2}{T}^{-2}$
2. $M^1{L}^{-3}{T}^{-2}$
3. $M^1{L}^2{T}^{-2}$
4. $M^1{L}^{-1}{T}^{-2}$

5.

Which of the following is dimensionally correct
1. Pressure = Energy per unit area
2. Pressure = Energy per unit volume
3. Pressure = Force per unit volume
4. Pressure = Momentum per unit volume per unit time

6.

The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are 
1. Mass, time
2. Time, length
3. Mass, length
4. Time, mole

7.

If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is  
1. $P{V}^2{T}^2$
2. $P^{-1}{V}^2{T}^{-2}$
3. $PV{T}^2$
4. $P^{-1}V{T}^2$

8.

The physical quantity which has dimensional formula as that of $\frac{\text{Energy}}{\text{Mass}\times \text{Length}}$is 
1. Force
2. Power
3. Pressure
4. Acceleration

9.

Which of the following represents the dimensions of Farad 
1. $M^{-1}{L}^{-2}{T}^4{A}^2$
2. $M{L}^2{T}^2{A}^{-2}$
3. $M{L}^2{T}^2{A}^{-1}$
4. $M{T}^{-2}{A}^{-1}$

10.

The dimensions of emf in MKS are-
1. $\left[M^0{L}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$
2. $\left[{\mathrm{ML}}^1{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$
3. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{A}}^{-1}\right]$
4. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$

11.

Pressure gradient has the same dimensions as that of:
1. Velocity gradient
2. Potential gradient
3. Energy gradient
4. None of these

12.

In the vernier callipers given below, \(9\) main scale divisions matched with \(10\) vernier scale divisions. Assume the edge of the vernier scale as the \('0'\) for the vernier scale. The thickness of the object using the defective vernier callipers will be:  
     
1. \(13.3\text{ mm}\)
2. \(13.4\text{ mm}\)
3. \(13.5\text{ mm}\)
4. \(13.6\text{ mm}\)

13.

In head on collision of two point particles, loss
in kinetic energy is given by 
$∆\mathrm{K}=\frac{{\mathrm{m}}_1{\mathrm{m}}_2}{2\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}{\left|\overrightarrow{{\mathrm{u}}_1}-\overrightarrow{{\mathrm{u}}_2}\right|}^2\left(1-{\mathrm{k}}^2\right)$
With usual notations (except k), the
dimensional formula of quantity k is
1. [M⁰L⁰T^–1] 
2. [M⁰L⁰T⁰]
3. [M⁰LT^–1] 
4. [M⁰L²T^–2]
 

14.

In the \({RL}\) circuit shown in the figure, a resistor \(R\) and an inductor \(L\) are connected in series with an AC source. The impedance \(Z\) of the circuit is expressed as: \({Z}^2={A}^2+{B}^2.\)
(\(A\) and \(B\) represent two quantities associated with the circuit elements)
         
The dimensions of the product \({AB}\) are:
1. \(\left[{M^1 L^2 T}^2 A^{-3}\right] \)
2. \(\left[{M^2 L^4 T^{-6} A^{-4}}\right]\)
3. \(\left[{ML^{-1} T^2 A}^{-3}\right]\)
4. \(\left[{M^{-1} L^{-2}T}^2{A}^4\right]\)

15.

If \(\int \frac{d x}{\sqrt{a^2-x^2}}=a^n \sin ^{-1} \frac{x}{a}\) is dimensionally correct, then the value of \(n\) will be:

1.	\(1\)	2.	\(\text{zero}\)
3.	\(\text-1\)	4.	\(2\)

16.

The expression for drift speed is ${\mathrm{v}}_{\mathrm{d}}=\frac{\mathrm{J}}{\mathrm{ne}}$
Here, J = current density,
n = number of electrons per unit volume,
e = $1.6\times {10}^{-\times 19}$ units
The units and dimensions of e are:
1. Coulomb and [AT]
2. Ampere per second and $\left[{\mathrm{AT}}^{-1}\right]$
3. No sufficient information
4. None of the above

17.

Which of the following ratios express pressure?
1. Force/Volume
2. Energy/Volume
3. Energy/Area
4. Force/length

18.

28. The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, the minimum inaccuracy in the measurement of distance:
$\left(1\right)<mspace\; width="1em"></mspace>0.02<mspace\; width="1em"></mspace>\mathrm{mm}$
$\left(2\right)<mspace\; width="1em"></mspace>0.2<mspace\; width="1em"></mspace>\mathrm{mm}$
$\left(3\right)<mspace\; width="1em"></mspace>0.1<mspace\; width="1em"></mspace>\mathrm{cm}$
$\left(4\right)<mspace\; width="1em"></mspace>0.01<mspace\; width="1em"></mspace>\mathrm{mm}$
 
 
 
 
This objective question is based on NCERT Exemplar subjective Question.

19.

30. If the unit of force is 100 N, the unit of length is 10 m, and the unit of time is 100 sec, what is the unit of mass in this system of units?
$\left(1\right)<mspace\; width="1em"></mspace>10<mspace\; width="1em"></mspace>\mathrm{kg}$
$\left(2\right)<mspace\; width="1em"></mspace>{10}^3<mspace\; width="1em"></mspace>\mathrm{kg}$
$\left(3\right)<mspace\; width="1em"></mspace>{10}^{-5}<mspace\; width="1em"></mspace>\mathrm{kg}$
$\left(4\right)<mspace\; width="1em"></mspace>{10}^{+5}<mspace\; width="1em"></mspace>\mathrm{kg}$
 
 
 
 
This objective question is based on NCERT Exemplar subjective Question.

20.

39. In the expression $\mathrm{P}={\mathrm{EL}}^2{\mathrm{m}}^{-5}{\mathrm{G}}^{-2}$, E, m, L, and G denote energy, mass, angular momentum, and gravițational constant, respectively. Dimensions of P are:
$\left(1\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$
$\left(2\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^1{\mathrm{L}}^0{\mathrm{T}}^{-2}\right]$
$\left(3\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\right]$
$\left(4\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^2{\mathrm{L}}^0{\mathrm{T}}^1\right]$
 
 
 
 
 
This objective question is based on NCERT Exemplar subjective Question.

21.

If P=2.348 cm and Q=2.1 cm, then P - Q equals=?
1. 0.248 cm
2. 0.25 cm
3. 0.2 cm
4. 0.3 cm

22.

We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be \(2.63~\text s, 2.56~\text s, 2.42~\text s, 2.71~\text s,\) and \(2.80~\text s.\) The average absolute error and percentage error, respectively, are:
1. \(0.22~\text s\) and \(4\%\)
2. \(0.11~\text s\) and \(4\%\)
3. \(4~\text s\) and \(0.11\%\)
4. \(5~\text s\) and \(0.22\%\)

23. The dimensional formula of viscous force is:
1. \( {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \)
2. \( {\left[\mathrm{ML} \mathrm{T}^{-2}\right]} \)
3. \( {\left[\mathrm{M} \mathrm{L^2} \mathrm{~T}^{-3}\right]} \)
4. \( {\left[\mathrm{M} \mathrm{L^0} \mathrm{~T}^{-1}\right]} \)

24. In Vander Wall's equation \(\left[{P}+\dfrac{{a}}{{V}^{2}}\right][{V}-{b}]={RT}\);  \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\dfrac a b\) is dimensionally equal to:

1.	\(\dfrac P V\)	2.	\(\dfrac V P\)
3.	\(PV\)	4.	\(PV^3\)

25. For a real gas the equation of gas is given by; \(\left({P+{{an^{2}}\over{V^{2}}}}\right)\left({V-bn}\right)=nRT\). If symbols have their usual meaning, then the dimensions of \({{V^{2}}\over{an^{2}}}\) is same as that of:
1. compressibility
2. bulk modulus
3. viscosity
4. energy density

26. \(n-\)divisions on the main scale of a vernier calipers coincide with \(n+1 \) divisions on the vernier scale. If each division on the main scale is of \(x\) units, determine the least count of the instrument:
1. \(\dfrac{x}{n}\)
2. \(\dfrac{x}{n+1}\)
3. \(\dfrac{x}{n-1}\)
4. \(\dfrac{2 x}{n+1}\)

27. The dimensions of a rectangular block measured with a vernier calliper having least count \(0.1 \text{ mm}\) is \(5.0 \mathrm{~mm} \times 10.0 \mathrm{~mm} \times 10.0 \mathrm{~mm} .\) The maximum percentage error in the measurement of volume of the bock is: 
1. \(5 \%\)
2. \(10 \%\)
3. \(15 \%\)
4. \(4 \%\)

28. What is the reading of the vernier scale shown in the figure?

1. \(60.7 \mathrm{~mm}\)
2. \(61.3 \mathrm{~mm}\)
3. \(62.4 \mathrm{~mm}\)
4. \(63.7 \mathrm{~mm}\)

29. A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001 \mathrm{~cm} \text {. }\)The main scale reading is \(5 \mathrm{~mm} \) and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of \(-0.004 \mathrm{~cm}\), the correct diameter of ball is: 
1. \(0.521 \mathrm{~cm}\)
2. \(0.525 \mathrm{~cm}\)
3. \(0.529 \mathrm{~cm}\)
4. \(0.053 \mathrm{~cm}\)
 

30. A micrometre (screw gauge) has a least count of \(0.02 ~\text{mm}.\) When the measuring faces are in contact, only the zero marking of the main scale is visible, and the \(6^{\mathrm {th }}\) division of the circular scale coincides with the reference line. The zero error of the instrument is:

1.	\(+0.12 ~\text{mm} \)	2.	\(-0.12 ~\text{mm} \)
3.	\(+0.60 ~\text{mm} \)	4.	\(-0.06 ~\text{mm} \)