Units, Dimensions & Measurements PYQs Set 7 (PDF)

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Set 7 of 10 · Questions 181-210 of 276

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NEET Physics · Units, Dimensions & Measurements · Set 7 (Q181-210)

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181.
The workdone by a gas molecule in an isolated system is given by, $W = α β^{2} e^{- \frac{x ^{2}}{α kT}}$ , where $x$ is thedisplacement, $k$ is the Boltzmann constant and $T$ is the temperature. $α$ and $β$ are constants. Then thedimensions of $β$ will be –
1. (1) $(M^{0} LT^{0})$
2. (2) $(M^{2} LT^{2})$
3. (3) $(MLT^{- 2})$
4. (4) $(ML^{2} T^{- 2})$
182.
Let $l, r, c$ and $v$ represent inductance, resistance, capacitanceand voltage, respectively. The dimension of $\frac{l}{rcv}$ in $SI$ unitswill be:
1. (1) $[LA^{- 2}]$
2. (2) $[A^{- 1}]$
3. (3) $[LTA]$
4. (4) $[LT^{2}]$
183.
Consider a spongy block of mass $m$ floating on a flowing river. The maximum mass of the block is related to the speed of the river flow $v$ , acceleration due to gravity $g$ and the density of the block $ρ$ such that $m_{max} = kvxgyρz$ ( $k$ is constant). The values of $x, y$ and $z$ should then respectively be(Mass of the spongy block is assumed to vary due to absorption of water by it)
1. (1) $6, 3, 2$
2. (2) $6, - 3, 1$
3. (3) $3, 6, 1$
4. (4) $6, 1, 3$
184.
$Match List-I with List-II. multi |c|List - I multicolumn 2c|List -II$
$List-I$ $column 2$
$(A) Magnetic Induction$ $(I) M L^{2} T^{- 2} A^{- 1}$
$(B) Magnetic Flux$ $(II) M^{0} L^{- 1} A$
$(C) Magnetic Permeability$ $(III) M T^{- 2} A^{- 1}$
$(D) Magnetization$ $(IV) M L T^{- 2} A^{- 2}$
$Choose the most appropriate answer from the options given below:$
1. (1) $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$
2. (2) $(A)-(II), (B)-(I), (C)-(IV),(D)-(III)$
3. (3) $(A)-(III),(B)-(II),(C)-(IV),(D)-(I)$
4. (4) $(A)-(III), (B)-(I), (C)-(IV), (D)-(II)$
185.
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be :
1. (1) $V^{-4} A^{2} F$
2. (2) $V^{-2} A^{2} F^{-2}$
3. (3) $V^{-4} A^{-2} F$
4. (4) $V^{-2} A^{2} F^{2}$
186.
Match List - I with List - II.
$List - I (A) Magnetic induction (B) Magnetic intensity (C) Magnetic flux (D) Magnetic moment List - II (I) Ampere meter 2 (II) Weber (III) Gauss (IV) Ampere/meter$
1. (1) $(A)-(I), (B)-(II), (C)-(III), (D)-(IV)$
2. (2) $(A)-(III), (B)-(IV), (C)-(I), (D)-(II)$
3. (3) $(A)-(III), (B)-(II), (C)-(I), (D)-(IV)$
4. (4) $(A)-(III), (B)-(IV), (C)-(II), (D)-(I)$
187.
If $1 %$ and $2 %$ are the errors in the measurement of mass and density of a cube respectively, then the error in the measurement of length is
1. (1) $1 %$
2. (2) $3 %$
3. (3) $2 %$
4. (4) $4 %$
188.
Which one of the following is the correct dimensional formula for the capacitance in F?
$M, L, T$ and C stand for unit of mass, length, time and charge,
1. (1) $[F] = C^{2} M^{- 1} L^{- 2} T^{2}$
2. (2) $[F] = C^{2} M^{- 2} L^{2} T^{2}$
3. (3) $[F] = C M^{- 2} L^{- 2} T^{- 2}$
4. (4) $[F] = C M^{- 1} L^{- 2} T^{2}$
189.
A force $F$ is applied on a square plate of length $L$ . If the percentage error in the determination of $L$ is $3 %$ and in $F$ is $4 %$ , then permissible error in the calculation of pressure is
1. (1) $13 %$
2. (2) $10 %$
3. (3) $7 %$
4. (4) $12 %$
190.
Choose the physical quantity pair with the same dimensions.
1. (1) $Angular momentum and work$
2. (2) $Work and torque$
3. (3) $Potential energy and linear momentum$
4. (4) $Kinetic energy and velocity$
191.
A quantity $f$ is given by $f = \frac{h c ^{5}}{G}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Plancks constant. Dimension of $f$ is that of :
1. (1) $Momentum$
2. (2) $Energy$
3. (3) $Force$
4. (4) $Pressure$
192.
The resultant $R$ of $P$ and $Q$ is perpendicular to $P$ . Also $| P | = | R |$ . The angle between $P$ and $Q$ is $(tan 45^{\circ} = 1)$
1. (1) $\frac{5 π}{4}$
2. (2) $\frac{7 π}{4}$
3. (3) $\frac{π}{4}$
4. (4) $\frac{3 π}{4}$
193.
Match List I with List II.
$List I A. Torque B. Stress C. Latent Heat D. Power List II I. N m s^{- 1} II. J k g^{- 1} III. Nm IV. N m^{- 2}$
Choose the correct answer from the options given below:
1. (1) $A-III, B-II, C-I, D-IV$
2. (2) $A-III, B-IV, C-II, D-I$
3. (3) $A-IV,B-I,C-III,D-II$
4. (4) $A-II,B-III, C-I, D-IV$
194.
The Vernier scale of a travelling microscope has 50 divisions which coincides with 49 main scale divisions. If each main scale division is $0.5 mm$ , then the least count of the microscope is
1. (1) $0.01 mm$
2. (2) $0.01 cm$
3. (3) $0.5 cm$
4. (4) $0.5 mm$
195.
If speed of light in vacuum $(3 \times 10^{8} ms^{- 1})$ , acceleration due to gravity ( $10 ms^{- 2}$ ) and mass of electron $(9.1 \times 10^{- 31} kg)$ are taken as fundamental physical quantities, then the unit of time in this system is
1. (1) $3 \times 10^{3} s$
2. (2) $5 \times 10^{- 19} s$
3. (3) $3 \times 10^{19} s$
4. (4) $3 \times 10^{7} s$
196.
Match List - I with List - II.
$List I (A) Mass density (B) Impulse (C) Power (D) Moment of inertia List II (I) M L^{2} T^{- 3} (II) M L T^{- 1} (III) M L^{2} T^{0} (IV) M L^{- 3} T^{0}$
Choose the correct answer from the options given below:
1. (1) $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
2. (2) $(A)-(II), (B)-(III), (C)-(IV), (D)-(I)$
3. (3) $(A)-(IV), (B)-(III), (C)-(I), (D)-(II)$
4. (4) $(A)-(IV), (B)-(II), (C)-(I), (D)-(III)$
197.
In $SI$ unit the dissmensions of $\frac{ϵ _{0}}{μ _{0}}$ is:
1. (1) $A^{- 1} TM L^{3}$
2. (2) $A T^{2} M^{- 1} L^{- 1}$
3. (3) $AT^{- 3} ML^{3/2}$
4. (4) $A^{2} T^{3} M^{- 1} L^{- 2}$
198.
The force of interaction between two atoms is given by $F = αβ exp (- \frac{x ^{2}}{αkT})$ where $x$ is the distance, $k$ is theBoltzmann constant and $T$ is temperature and $α$ and $β$ are two constants. The dimension of $β$ is:
1. (1) $M^{0} L^{2} T^{- 4}$
2. (2) $M^{2} LT^{- 4}$
3. (3) $MLT^{- 2}$
4. (4) $M^{2} L^{2} T^{- 2}$
199.
A person measures mass of 3 different particles as $435.42 g, 226.3 g$ and 0.125 g. According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.
1. (1) $661.845 g$
2. (2) $661.84 g$
3. (3) $662 g$
4. (4) $661.8 g$
200.
The dimensional formula of physical quantity is $M^{a} L^{b} T^{c}$ . Then that physical quantity is
1. (1) $surface tension if a = 1, b = 1, c = - 2$
2. (2) $force if a = 1, b = 1, c = 2$
3. (3) $angular frequency if a = 0, b = 0, c = - 1$
4. (4) $spring constant if a = 1, b = - 1, c = - 2$
201.
Match List I with List II
$List-I (A) Torque (I) M L^{- 2} T^{- 2} (C) Pressure gradient (III) M L^{- 1} T^{- 1} List-II (B) Stress (II) M L^{2} T^{- 2} (D) Coefficient of viscosity (IV) M L^{- 1} T^{- 2}$
Choose the correct answer from the options given below :
1. (1) $A-II, B-I, C-IV, D-III$
2. (2) $A-IV, B-II, C-III, D-I$
3. (3) $A-II, B-IV, C-I, D-III$
4. (4) $A-III, B-IV, C-I, D-II$
202.
Which of the following has the dimensions of pressure?
1. (1) $[ML T^{- 2}]$
2. (2) $[M L^{- 1} T^{- 2}]$
3. (3) $[M L^{- 2} T^{- 2}]$
4. (4) $[M^{- 1} L^{- 1}]$
203.
The maximum percentage error in the measurment of density of a wire is [Given, mass of
wire $= (0.60 \pm 0.003) g$ radius of wire $= (0.50 \pm 0.01) cm$ length of wire $= (10.00 \pm 0.05) cm]$
1. (1) $8$
2. (2) $5$
3. (3) $4$
4. (4) $7$
204.
If E and $E_{0}$ denote energies at time t and t0 respectively, and L and $L_{0}$ distance from some point at t and t0 respectively, then which of the following equations can be declared to be incorrect on dimensional grounds.(A) $E = \frac{2 E _{0} L}{L _{0} - L}$ (B) $E = E_{0} e^{- 2 L / L_{0}}$ (C) $E = 2 L e^{L_{0}} - L / E_{0}$ (D) $E = 2 (E_{0} / L_{0}) \times e^{- L / L_{0}}$
1. (1) $A, B only$
2. (2) $A, C only$
3. (3) $A, C, D only$
4. (4) $C, D only$
205.
In a vernier callipers, $(N + 1)$ divisions of vernier scale coincide with $N$ divisions of main
scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is: [NEET 2024]
1. (1) $\frac{1}{10 N}$
2. (2) $\frac{1}{100 ( N + 1 )}$
3. (3) $100 N$
4. (4) $10 (N + 1)$
206.
A physical quantity $Q$ is found to depend on observables $x, y$ and $z$ , obeying relation $Q = \frac{x ^{3} y ^{2}}{z}$ . The percentage error in the measurements of $x, y$ and $z$ are $1 %, 2 %$ and $4 %$ respectively. What is percentage error in the quantity $Q$ ?
1. (1) $11 %$
2. (2) $4 %$
3. (3) $1 %$
4. (4) $3 %$
207.
One main scale division of a vernier caliper is equal to $m$ units. If $n^{th}$ division of main scale coincides with $(n + 1)^{th}$ division of vernier scale, the least count of the vernier caliper is :
1. (1) $\frac{n}{( n + 1 )}$
2. (2) $\frac{1}{( n + 1 )}$
3. (3) $\frac{m}{( n + 1 )}$
4. (4) $\frac{m}{n ( n + 1 )}$
208.
The physical quantity having the dimensions $(M^{- 1} L^{- 3} T^{3} A^{2})$ is
1. (1) $resistance$
2. (2) $resistivity$
3. (3) $electrical conductivity$
4. (4) $electromotive force.$
209.
If E,L,M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P= $E L^{2} M^{- 5} G^{- 2}$ are :-
1. (1) $[M^{0} L^{1} T^{0}]$
2. (2) $[M^{- 1} L^{- 1} T^{2}]$
3. (3) $[M^{1} L^{1} T^{- 2}]$
4. (4) $[M^{0} L^{0} T^{0}]$
210.
An expression for a dimensionless quantity P is given by $P = \frac{α}{β} lo g_{e} (\frac{k t}{β x})$ ; where $α$ and $β$ are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $α$ will be :
1. (1) $[M° L^{- 1} T°]$
2. (2) $[ML° T^{- 2}]$
3. (3) $[M L T^{- 2}]$
4. (4) $[M L^{2} T^{- 2}]$