Units, Dimensions & Measurements PYQs Set 10 (PDF)

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Set 10 of 10 · Questions 271-294 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 10 (Q271-294)
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271. $Identify the pair of physical quantities that have same dimensions :$ (1) $velocity gradient and decay constant$ (2) $wien's constant and Stefan constant$ (3) $angular frequency and angular momentum$ (4) $wave number and Avogadro number$ 272. $If P, Q and R are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?$ (1) $\frac{PQ}{R}$ (2) $\frac{P - Q}{R}$ (3) $\frac{PR - Q ^{2}}{R}$ (4) $PQ - R$ 273. $Identify the pair of physical quantities which have different dimensions :$ (1) $Wave number and Rydberg's constant$ (2) $Stress and Coefficient of elasticity$ (3) $Coercivity and Magnetisation$ (4) $Specific heat capacity and Latent heat$ 274. $Given below are two statements : One is labelled as Assertion (a) and other is labelled as Reason (R). Assertion (a) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is p and radius of the drop is r, then is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. choose the correct answer from the options given below.$ (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) $(a) is false but (R) is true$ 275. $Match List I with List II.$ (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) $(a) \to (i), (b) \to (iv), (c) \to (ii), (d) \to (iii)$ 276. $A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is :$ (1) $4.40 %$ (2) $3.40%$ (3) $2.40%$ (4) $5.40%$ 277. $In Vander Waals equation [P + \frac{a}{V ^{2}}] [V - b] = R T; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants \frac{a}{b} is dimensionally equal to :$ (1) $\frac{P}{V}$ (2) $\frac{V}{P}$ (3) $PV$ (4) $P V^{3}$ 278. $If 400 Ω of resistance is made by adding four 100 Ω resistances of tolerance 5%, then the tolerance of the combination is :$ (1) $5%$ (2) $10 %$ (3) $15 %$ (4) $20 %$ 279. $The number of significant figures in the measurement of a length 0.079000 m is$ (1) $7$ (2) $2$ (3) $5$ (4) $4$ 280. $Electric field in a certain region is given by E = \frac{A}{x ^{2}} i^+ \frac{B}{y ^{3}} j^. The SI unit of A and B are :$ (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) $N m^{2} C; N m^{3} C$ 281. $If R, X_{L} . and X_{c} represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:$ (1) $R X_{L} X_{c}$ (2) $\frac{R}{X _{L} X _{C}}$ (3) $\frac{R}{X _{L} X _{C}}$ (4) $R \frac{X _{L}}{X _{C}}$ 282. $The force is given in terms of time t and displacement x by the equation F = AcosBx + CsinDt. The dimensional formula of \frac{A D}{B} is :$ (1) $[M^{0} L T^{- 1}]$ (2) $[M L^{2} T^{- 3}]$ (3) $[M^{1} L^{1} T^{- 2}]$ (4) $[M^{2} L^{2} T^{- 3}]$ 283. $The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v = r^{a} ρ^{b} s^{c} . The values of a, b and c respectively are$ (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) $(- \frac{3}{2}, \frac{1}{2}, \frac{1}{2})$ 284. $The dimensions of (\frac{B ^{2}}{μ _{0}}) will be : (if μ_{0} : permeability of free space and B : magnetic field)$ (1) $[M L^{2} T^{- 2}]$ (2) $[M L T^{- 2}]$ (3) $[M L^{- 1} T^{- 2}]$ (4) $[M L^{2} T^{- 2} A^{- 1}]$ 285. $Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R). Assertion (A): In Vernier caliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R): The zero error in Vernier Caliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :$ (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) $(A) is false but (R) is true$ 286. $The number of significant figures in 4.870 m is$ (1) $3$ (2) $4$ (3) $2$ (4) $1$ 287. $Which of the following dimensions will be the same as that of time?$ (1) $\frac{L}{R}$ (2) $\frac{C}{L}$ (3) $LC$ (4) $\frac{R}{L} .$ 288. $Choose the correct statement from following.$ (1) $Not all basic laws of physics are universal$ (2) $Conservation laws have a deep connection with symmetries of nature$ (3) $There are four to six fundamental forces in nature that govern the diverse phenomena of the world$ (4) $Physics can generate new technology but new physics cannot come out from technology$ 289. $What will be the projection of vector A = i^+ j^+ k^on vector B = i^+ j^?$ (1) $2 (i^+ j^+ k^)$ (2) $2 (i^+ j^+ k^)$ (3) $2 (i^+ j^)$ (4) $(i^+ j^)$ 290. $If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :$ (1) $[F T^{- 1} V^{- 1}]$ (2) $[F T V^{- 1}]$ (3) $[F T^{2} V]$ (4) $[F V T^{- 1}]$ 291. $An expression of energy density is given by u = \frac{α}{β} sin (\frac{α x}{k t}), where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be :$ (1) $[M L^{2} T^{- 2} θ^{- 1}]$ (2) $[M^{0} L^{2} T^{- 2}]$ (3) $[M°L°T°]$ (4) $[M° L^{2} T°]$ 292. $Let ℓ, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of \frac{ℓ}{r c v} in SI units will be :$ (1) $[L T^{2}]$ (2) $[L A^{-2}]$ (3) $[LTA]$ (4) $[A^{-1}]$ 293. $(P + \frac{a}{V ^{2}}) (V - b) = RT represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, h, R are the constants. The physical quantity, which has dimensional formula as that of \frac{b ^{2}}{a}, will be :$ (1) $Bulk modulus$ (2) $Modulus of rigidity$ (3) $Compressibility$ (4) $Energy density$ 294. $Three particles P,Q and R are moving along the vectors A = i^+ j^, B = j^+ k^and C = - i^+ j^respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector A and B . Similarly particle Q is moving normal to the plane which contains vector A and C . The angle between the direction of motion of P and Q is cos^{- 1} (\frac{1}{x}) . Then the value of x is _____.$