Units, Dimensions & Measurements PYQs Set 7 (PDF)

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Set 7 of 10 · Questions 181-210 of 294

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

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181.
Match the LIST-I with LIST-II
$List-I (A) Magnetic induction (B) Magnetic flux (C) Magnetic permeability (D) Self inductance List-II (I) ML T^{- 2} A^{- 2} (II) ML^{2} T^{- 2} A^{- 2} (III) ML^{0} T^{- 2} A^{- 1} (IV) ML^{2} T^{- 2} A^{- 1}$
Choose the correct answer from the options given below:
1. (1) $A-III, B-IV, C-II, D-I$
2. (2) $A-III, B-IV, C-I, D-II$
3. (3) $A-IV, B-III, C-I, D-II$
4. (4) $A-I, B-III, C-IV, D-II$
182.
If absolute error is $0.05 m$ for a measured length of $5 m$ . What is the percentage error?
1. (1) $1 %$
2. (2) $2 %$
3. (3) $3 %$
4. (4) $4 %$
183.
Stopping potential depends on Planks constant $(h),$ current $(I),$ Universal gravitational constant $(G)$ and speed of light $(C)$ . Choose the correct option for the dimension of stopping potential $(V)$
1. (1) $h I^{- 1} G^{1} C^{5}$
2. (2) $h^{- 1} I^{1} G^{- 1} C^{6}$
3. (3) $h^{0} I^{1} G^{1} C^{6}$
4. (4) $h^{0} I^{- 1} G^{- 1} C^{5}$
184.
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 $3$ division 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 the sheet is:
1. (1) $5.755 mm$
2. (2) $5.950 mm$
3. (3) $5.725 mm$
4. (4) $5.740 mm$
185.
Which of the following is the unit of mobility of a electron in a conductor?
1. (1) $k g^{- 1} s^{2} A^{- 1}$
2. (2) $kg^{- 1} s^{2} A$
3. (3) $kg^{- 1} ms^{2} A^{- 1}$
4. (4) $kg ms^{- 1} A^{- 1}$
186.
The dimensions of $\frac{B ^{2}}{2 μ _{o}}$ ,where $B$ is magnetic field and $μ_{o}$ is the magnetic permeability of vacuum, is
1. (1) $M L^{- 1} T^{- 2}$
2. (2) $M L^{2} T^{- 2}$
3. (3) $M L^{- 1} T^{2}$
4. (4) $M L^{- 2} T^{- 1}$
187.
In SI units, $kg m^{2} s^{- 2}$ is equivalent to which of the following?
1. (1) $newton$
2. (2) $watt$
3. (3) $joule$
4. (4) $pascal$
188.
If $F_{1}, F_{2}$ and $F_{3}$ are the relative strengths of the gravitational, the weak nuclear and the electromagnetic forces respectively, then
1. (1) $F_{1} > F_{2} > F_{3}$
2. (2) $F_{1} < F_{2} < F_{3}$
3. (3) $F_{1} = F_{2} = F_{3}$
4. (4) $F_{2} > F_{3} > F_{1}$
189.
List - I with List II.
$List I (A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility List II (I) M L^{0} T^{- 3} (II) M L^{- 2} T^{- 2} (III) M^{- 1} L T^{2} (IV) M L^{- 1} T^{- 1}$
1. (1) $(A)-(II), (B)-(III), (C)-(IV), (D)-(I)$
2. (2) $(A)-(IV), (B)-(II), (C)-(I), (D)-(III)$
3. (3) $(A)-(IV), (B)-(I), (C)-(II), (D)-(III)$
4. (4) $(A)-(I), (B)-(IV), (C)-(III), (D)-(II)$
190.
Among the following the least unit for length is
1. (1) $parsec$
2. (2) $nanometer$
3. (3) $fermi$
4. (4) $angstrom$
191.
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) $(ML^{2} T^{- 2})$
192.
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) $[LT^{2}]$
193.
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) $6, 1, 3$
194.
$Match List-I with List-II. multi |c|List - I multicolumn 2c|List -II$
$List-I$ $column 2$
$(A) Magnetic Induction$ $(I) M L^{2} T^{- 2} A^{- 1}$
$(B) Magnetic Flux$ $(II) M^{0} L^{- 1} A$
$(C) Magnetic Permeability$ $(III) M T^{- 2} A^{- 1}$
$(D) Magnetization$ $(IV) M L T^{- 2} A^{- 2}$
$Choose the most appropriate answer from the options given below:$
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) $(A)-(III), (B)-(I), (C)-(IV), (D)-(II)$
195.
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) $V^{-2} A^{2} F^{2}$
196.
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) $(A)-(III), (B)-(IV), (C)-(II), (D)-(I)$
197.
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) $4 %$
198.
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) $[F] = C M^{- 1} L^{- 2} T^{2}$
199.
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) $12 %$
200.
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) $Kinetic energy and velocity$
201.
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) $Pressure$
202.
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) $\frac{3 π}{4}$
203.
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) $A-II,B-III, C-I, D-IV$
204.
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) $0.5 mm$
205.
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) $3 \times 10^{7} s$
206.
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) $(A)-(IV), (B)-(II), (C)-(I), (D)-(III)$
207.
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) $A^{2} T^{3} M^{- 1} L^{- 2}$
208.
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) $M^{2} L^{2} T^{- 2}$
209.
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) $661.8 g$
210.
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) $spring constant if a = 1, b = - 1, c = - 2$