Units, Dimensions & Measurements PYQs Set 9 (PDF)

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Mere Teacher · Previous Year Questions NEET Physics · Units, Dimensions & Measurements · Set 9 (Q241-270)
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241. $The unit of magnetic induction is$ (1) $Wb m^{- 2}$ (2) $Wb m^{- 1}$ (3) $WbA$ (4) $Wb$ 242. $In a Vernier Calipers. 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4^{t h} Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6^{t h} Vernier scale division exactly, coincides with the main scale reading. The diameter of the spherical body will be:$ (1) $3.02 cm$ (2) $3.06 cm$ (3) $3.10 cm$ (4) $3.20 cm$ 243. $When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4^{th} mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5^{th} division of vernier scale coincides with a main scale division. Measured length of cylinder is____mm. (Least count of Vernier calliper = 0.1 mm)$ (1) $15.5$ (2) $15.9$ (3) $15.1$ (4) $15.4$ 244. $The dimensions of RC is$ (1) $square of time$ (2) $square of inverse time$ (3) $time$ (4) $inverse time.$ 245. $Match the physical quantities given in List-I with dimensions in List-II. List I A. Gravitational constant B. Stefan’s constant C. Permitivity D. Specific heat capacity List II (i) (M^{0} L^{2} T^{- 2} K^{- 1}) (ii) (M^{- 1} L^{3} T^{- 2}) (iii) (ML^{0} T^{- 3} K^{- 4}) (iv) (M^{- 1} L^{- 3} T^{4} I^{2}) (The dimension of mass, length, time, temperature and current are M, L, T, K and I, respectively). The correct match is A B C D$ (1) $IV I III II$ (2) $I IV II III$ (3) $III II I IV$ (4) $II III IV I$ 246. $A student determined Young's Modulus of elasticity using the formula The value of g is taken to be 9.8m/, without any significant error, his observation are as following. Physical Quantity Least count of the Equipment used for measurement Observed value Mass(M) 1 g 2 kg Length of bar(L) 1 mm 1 m Breadth of bar(b) 0.1 mm 4 cm Thickness of bar(d) 0.01 mm 0.4 cm Depression(8) 0.01 mm 5 mm Then the fractional error in the measurement Y of is:$ (1) $0.0083$ (2) $0.0155$ (3) $0.155$ (4) $0.083$ 247. $The least count of the main scale of a vernier callipers is 1 mm . Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7^{th} division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4^{th} VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)$ (1) $3.21 cm$ (2) $2.99 cm$ (3) $3.07 cm$ (4) $3.2 cm$ 248. $Match List I with List II: List-I (Physical Quantity) A. Pressure gradient B. Energy density C. Electric Field D. Latent heat List-II (Dimensional Formula) I. [M^{0} L^{2} T^{- 2}] II. [M^{1} L^{- 1} T^{- 2}] III. [M^{1} L^{- 2} T^{- 2}] IV. [M^{1} L^{1} T^{- 3} A^{- 1}] Choose the correct answer from the options given below:$ (1) $A-III,B-II,C-I,D-IV$ (2) $A-II, B-III, C-IV, D-I$ (3) $A-III, B-II, C-IV, D-I$ (4) $A-II, B-III, C-I, D-IV$ 249. $A physical quantity 'y' is represented by the formula y = m^{2} r^{- 4} g^{x} l^{- \frac{3}{2}} If the percentage errors found in y,m,r,l and g are18,1,0,5,4 and p respectively, then find the value of x and p.$ (1) $5 and \pm 2$ (2) $4 and \pm 3$ (3) $\frac{16}{3} and \pm \frac{3}{2}$ (4) $8 and \pm 2$ 250. $Unit of pole strength of a magnet is$ (1) $Am^{- 1}$ (2) $Am^{2}$ (3) $Am^{- 2}$ (4) $Am$ 251. $Statement : 1 If three forces F_{1}, F_{2} and F_{3} are represented by three sides of a triangle and F_{1} + F_{2} = - F_{3}, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : II A triangle made up of three forces F_{1}, F_{2} and F_{3} as its sides taken in the same order, satisfy the condition for translatory equilibrium. choose the most appropriate answer from the options given below:$ (1) $Statement-I is false but Statement-II is true$ (2) $Statement-I is true but Statement-II is false$ (3) $Both Statement-I and Statement-II are false$ (4) $Both Statement-I and Statement-II are true.$ 252. $The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be$ (1) $[M L^{- 1} T^{- 1}]$ (2) $[M L^{- 1} T^{- 2}]$ (3) $[M L^{2} T^{- 1}]$ (4) $[M^{- 1} L^{3} T^{0}]$ 253. $The dimension of mutual inductance is :$ (1) $[M L^{2} T^{- 2} A^{- 1}]$ (2) $[M L^{2} T^{- 3} A^{- 1}]$ (3) $[M L^{2} T^{- 2} A^{- 2}]$ (4) $[M L^{2} T^{- 3} A^{- 2}]$ 254. $Identify the pair of physical quantities that have same dimensions :$ (1) $velocity gradient and decay constant$ (2) $wien's constant and Stefan constant$ (3) $angular frequency and angular momentum$ (4) $wave number and Avogadro number$ 255. $If P, Q and R are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?$ (1) $\frac{PQ}{R}$ (2) $\frac{P - Q}{R}$ (3) $\frac{PR - Q ^{2}}{R}$ (4) $PQ - R$ 256. $Identify the pair of physical quantities which have different dimensions :$ (1) $Wave number and Rydberg's constant$ (2) $Stress and Coefficient of elasticity$ (3) $Coercivity and Magnetisation$ (4) $Specific heat capacity and Latent heat$ 257. $Given below are two statements : One is labelled as Assertion (a) and other is labelled as Reason (R). Assertion (a) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is p and radius of the drop is r, then is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. choose the correct answer from the options given below.$ (1) $Both (a) and (R) are true and (R) is the correct explanation of (a)$ (2) $Both (a) and (R) are true but (R) is not the correct explanation of (a)$ (3) $(a) is true but (R) is false$ (4) $(a) is false but (R) is true$ 258. $Match List I with List II.$ (1) $(a) \to (iv), (b) \to (i), (c) \to (iii), (d) \to (ii)$ (2) $(a) \to (iv), (b) \to (iii), (c) \to (i), (d) \to (ii)$ (3) $(a) \to (iii), (b) \to (ii), (c) \to (iv), (d) \to (i)$ (4) $(a) \to (i), (b) \to (iv), (c) \to (ii), (d) \to (iii)$ 259. $A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is :$ (1) $4.40 %$ (2) $3.40%$ (3) $2.40%$ (4) $5.40%$ 260. $In Vander Waals equation [P + \frac{a}{V ^{2}}] [V - b] = R T; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants \frac{a}{b} is dimensionally equal to :$ (1) $\frac{P}{V}$ (2) $\frac{V}{P}$ (3) $PV$ (4) $P V^{3}$ 261. $If 400 Ω of resistance is made by adding four 100 Ω resistances of tolerance 5%, then the tolerance of the combination is :$ (1) $5%$ (2) $10 %$ (3) $15 %$ (4) $20 %$ 262. $The number of significant figures in the measurement of a length 0.079000 m is$ (1) $7$ (2) $2$ (3) $5$ (4) $4$ 263. $Electric field in a certain region is given by E = \frac{A}{x ^{2}} i^+ \frac{B}{y ^{3}} j^. The SI unit of A and B are :$ (1) $N m^{3} C^{- 1}; N m^{2} C^{- 1}$ (2) $N m^{2} C^{- 1}; N m^{3} C^{- 1}$ (3) $N m^{3} C; N m^{2} C$ (4) $N m^{2} C; N m^{3} C$ 264. $If R, X_{L} . and X_{c} represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:$ (1) $R X_{L} X_{c}$ (2) $\frac{R}{X _{L} X _{C}}$ (3) $\frac{R}{X _{L} X _{C}}$ (4) $R \frac{X _{L}}{X _{C}}$ 265. $The force is given in terms of time t and displacement x by the equation F = AcosBx + CsinDt. The dimensional formula of \frac{A D}{B} is :$ (1) $[M^{0} L T^{- 1}]$ (2) $[M L^{2} T^{- 3}]$ (3) $[M^{1} L^{1} T^{- 2}]$ (4) $[M^{2} L^{2} T^{- 3}]$ 266. $The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v = r^{a} ρ^{b} s^{c} . The values of a, b and c respectively are$ (1) $(- \frac{3}{2}, - \frac{1}{2}, \frac{1}{2})$ (2) $(\frac{3}{2}, - \frac{1}{2}, \frac{1}{2})$ (3) $(\frac{3}{2}, \frac{1}{2}, - \frac{1}{2})$ (4) $(- \frac{3}{2}, \frac{1}{2}, \frac{1}{2})$ 267. $The dimensions of (\frac{B ^{2}}{μ _{0}}) will be : (if μ_{0} : permeability of free space and B : magnetic field)$ (1) $[M L^{2} T^{- 2}]$ (2) $[M L T^{- 2}]$ (3) $[M L^{- 1} T^{- 2}]$ (4) $[M L^{2} T^{- 2} A^{- 1}]$ 268. $Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R). Assertion (A): In Vernier caliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R): The zero error in Vernier Caliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both (A) and (R) are correct and (R) is the correct explanation of (A)$ (2) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (3) $(A) is true but (R) is false$ (4) $(A) is false but (R) is true$ 269. $The number of significant figures in 4.870 m is$ (1) $3$ (2) $4$ (3) $2$ (4) $1$ 270. $Which of the following dimensions will be the same as that of time?$ (1) $\frac{L}{R}$ (2) $\frac{C}{L}$ (3) $LC$ (4) $\frac{R}{L} .$