1. The area of a rectangular field (in m² ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is

(1).138 × 10¹

(2). 1382

(3). 1382.5

(4). 14 × 10²

2. The percentage error in the measurement of g is:(Given that g = 4π²LT ² , L = (10 ± 0.1) cm, T = (100 ± 1)s )

(1).7%

(2). 2%

(3). 5%

(4). 3%

3. If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

(1).[F ] [A] [T ]

(2). [F ] [A] [T ²]

(3). [F ] [A] [T ⁻¹]

(4). [F ] [A⁻¹] [T ]

4. If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of

(1).[M²] [L⁻¹] [T ⁰]

(2). [M ] [L⁻¹] [T ⁻¹]

(3). [M ] [L⁰] [T ⁰]

(4). [M²] [L⁻²] [T ⁻¹]

5. Dimensions of stress are :

(1).[M L² T ⁻²]

(2). [M L⁰ T ⁻²]

(3). [M L⁻¹ T ⁻²]

(4). [M L T ⁻²]

6. Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 ?

(1).9.98 m

(2). 9.980 m

(3). 9.9 m

(4). 9.9801 m

7. In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where \(\displaystyle X = \frac{A^2B^{1/2}}{C^{1/3}D^3}\) will be

(1).10%

(2). (3/13) %

(3). 16%

(4). -10%

8. Planck’s constant (h), speed of light in vacuum (c) and Newton’sgravitational constant (G) are three fundamental constants. Which ofthe following combinations of these has the dimension of length ?

(1).

(2).

(3).

(4).

9. If dimensions of critical velocity v_c of a liquid flowing through a tube areexpressed as [η^xρ^yγ^z] where η, ρ and γ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by.

(1).-1,-1,-1

(2). 1,1,1

(3). 1,-1,-1

(4). -1,-1,1

10. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

(1).[F V T⁻¹]

(2). [F V T ⁻²]

(3). [F V⁻¹ T ⁻¹]

(4). [F V⁻¹ T ]

11. The quantities which have the same dimensions as those of solid angle are:

(1).strain and angle

(2). stress and angle

(3). strain and arc

(4). angular speed and stress

12. A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:

(1).\(\displaystyle \frac{\beta t}{\alpha}\)

(2). \(\displaystyle \frac{\alpha t}{\beta}\)

(3). \(\displaystyle \alpha \beta t\)

(4). \(\displaystyle \frac{\alpha \beta}{t}\)

13. The potential energy of a particle moving along x-direction varies as

The dimensions of A²B are:

(1).[M^3∕2L^1∕2T⁻³]

(2). [M^1∕2LT⁻³]

(3). [M²L^1∕2T⁻⁴]

(4). [ML²T⁻⁴]

14. The mechanical quantity, which has dimensions of reciprocal ofmass (M⁻¹) is :

(1).angular momentum

(2). coefficient of thermal conductivity

(3). torque

(4). gravitational constant

15. The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are

(1).Personal errors

(2). Least count errors

(3). Random errors

(4). Instrumental errors

16. A metal wire has mass (0.4 ± 0.002)g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be

(1).1.30%

(2). 1.60%

(3). 1.40%

(4). 1.20%

17. Plane angle and solid angle have

(1).Units but no dimensions

(2). Dimensions but no units

(3). No units and no dimensions

(4). Both units and dimensions

18. The physical quantity that has the same dimensional formula as pressure is:

(1).Coefficient of viscosity

(2). Force

(3). Momentum

(4). Young's modulus of elasticity

19. The unit of thermal conductivity is

(1).\(Wm^{−1}K^{−1}\)

(2). \(JmK^{−1}\)

(3). \(Jm^{−1}K^{ −1}\)

(4). \(WmK^{−1}\)

20. A physical quantity of the dimensions of length that can be formed out of c, G and e²/4πε0 is
[c is velocity of light, G is the universal constant of gravitation and e is charge]

(1).

(2).

(3).

(4).

21. IF energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

(1).[ \(Ev^{-2}T^{-1}\) ]

(2). [ \(Ev^{-1}T^{-2}\) ]

(3). [ \(Ev^{-2}T^{-2}\) ]

(4). [ \(E^{-2}v^{-1}T^{-3}\) ]

22. A baloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density \(\rho\) and takes a spherical share of radius R. When the gas is allowed to flow freely out of it, its radius r changes from R to 0 (zero) in time T. If the speed v(r) of gas coming out of the balloon depends on r as \(r^a\) and \(\text{T} \propto \text{S}^\alpha \text{A}^\beta \rho^\gamma \text{R}^\delta\) then

(1).\(\text{a}=\frac{1}{2} \text{,}\, \alpha=\frac{1}{2} \text{,}\, \beta=\frac{1}{2} \text{,}\, \gamma=\frac{1}{2} \text{,}\, \delta=\frac{7}{2}\)

(2). \( \text{a}=\frac{1}{2} \text{,}\, \alpha=\frac{1}{2} \text{,}\, \beta= -1 \text{,}\, \gamma=+1 \text{,}\, \delta=\frac{3}{2}\)

(3). \( \text{a}=\frac{1}{2} \text{,}\, \alpha=-\frac{1}{2}\text{,}\, \beta=-1 \text{,}\, \gamma=\frac{1}{2} \text{,}\, \delta=\frac{5}{2}\)

(4). \(\text{a}=-\frac{1}{2} \text{,}\, \alpha=-\frac{1}{2}\text{,}\, \beta=-1 \text{,}\, \gamma=\frac{1}{2} \text{,}\, \delta=\frac{7}{2}\)

23. A physical quantity P is related to four observations a, b, c, and d as follows:
\(\text{P}\,=\,\text{a}^3\text{b}^2 / \text{c} \sqrt{d}\)
The percentage errors of measurement in a, b, c, and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is

(1).15%

(2). 10%

(3). 2%

(4). 13%