Bottom of Pyramid - Test # 20 - Units & Dimensions

What are the dimensions of latent heat?
(1) $M L^{2} T^{- 2}$
(2) $M L^{- 2} T^{- 2}$
(3) $M^{0} L T^{- 2}$
(4) $M^{0} L^{2} T^{- 2}$

The dimensional formula of pressure is:
1. $\left[MLT^{-2}\right]$
2. $\left[ML^{-1}T^{2}\right]$
3. $\left[ML^{-1}T^{-2}\right]$
4. $\left[MLT^{2}\right]$

A light-year is a unit of:
1. Time
2. Mass
3. Distance
4. Energy

Which of the following is not equal to watt ?
(1) Joule/second
(2) Ampere $\times$ volt
(3) (Ampere)² $\times$ ohm
(4) Ampere/volt

A suitable unit for gravitational constant is:
(1) $k g - m \sec^{- 1}$
(2) $N m^{- 1} \sec$
(3) $N m^{2} k g^{- 2}$
(4) $k g m \sec^{- 1}$

The unit of angular acceleration in the SI system is
(1) $N k g^{- 1}$
(2) $m s^{- 2}$
(3) $r a d s^{- 2}$
(4) $m k g^{- 1} K$

Joule-second is the unit of :
(1) Work
(2) Momentum
(3) Pressure
(4) Angular momentum

A cube has a numerically equal volume and surface area. The volume of such a cube is :
1. 216 units
2. 1000 units
3. 2000 units
4. 3000 units

Electron volt is a unit of
(1) Charge
(2) Potential difference
(3) Momentum
(4) Energy

10.

Temperature can be expressed as a derived quantity in terms of any of the following:

1.	Length and mass	2.	Mass and time
3.	Length, mass, and time	4.	None of the above

11.

The density of wood is $0 .5 g m / c c$ in the CGS system of units. The corresponding value in MKS units is :
(1) 500
(2) 5
(3) 0.5
(4) 5000

12.

Which is the correct unit for measuring nuclear radii
(1) Micron
(2) Millimetre
(3) Angstrom
(4) Fermi

13.

Volt/metre is the unit of
(1) Potential
(2) Work
(3) Force
(4) Electric field intensity

14.

The velocity of a particle depends upon as $v = a + b t + c t^{2}$ ; if the velocity is in $m / \sec$ , the unit of a will be
(1) $m / \sec$
(2) $m / \sec^{2}$
(3) $m^{2} / \sec$
(4) $m / \sec^{3}$

15.

If the unit of length and force be increased four times, then the unit of energy is
1. Increased 4 times
2. Increased 8 times
3. Increased 16 times
4. Decreased 16 times

16.

The unit of specific resistance is
(1) Ohm / cm²
(2) Ohm / cm
(3) Ohm - cm
(4) (Ohm - cm)^-1

17.

If $u_1$ and $u_2$ are the units selected in two systems of measurement and $n_1$ and $n_2$ are their numerical values, then:

1.	$n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
2.	$n_1u_1+n_2u_2=0$
3.	$n_1n_2=u_1u_2$
4.	$(n_1+u_1)=(n_2+u_2)$

18.

If $x = a t + b t^{2}$ , where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b are
(1) $k m / s$
(2) $k m - s$
(3) $k m / s^{2}$
(4) $k m - s^{2}$

19.

Given the equation $\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}$. The units of $a$ will be: (where $P$ is pressure and $V$ is volume)
1. $\text{dyne} \times \text{cm}^5$
2. $\text{dyne} \times \text{cm}^4$
3. $\text{dyne} / \text{cm}^3$
4. $\text{dyne} / \text{cm}^2$

20.

Which is not a unit of electric field
(1) $N C^{- 1}$
(2) $V m^{- 1}$
(3) $J C^{- 1}$
(4) $J C^{- 1} m^{- 1}$

21.

Faraday is the unit of
(1) Charge
(2) emf
(3) Mass
(4) Energy

22.

Unit of surface tension is
(1) $N m^{- 1}$
(2) $N m^{- 2}$
(3) $N^{2} m^{- 1}$
(4) $N m^{- 3}$

23.

The dimensions of calorie are
1. $M L^{2} T^{- 2}$
2. $M L T^{- 2}$
3. $M L^{2} T^{- 1}$
4. $M L^{2} T^{- 3}$

24.

Dimensions of one or more pairs are same. Identify the pairs
(1) Torque and work
(2) Angular momentum and work
(3) Energy and Young's modulus
(4) Year and wavelength

25.

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type $f = C m^{x} K^{y}$ ; where C is a dimensionless quantity. The value of x and y are
1. $x = \frac{1}{2}, y = \frac{1}{2}$
2. $x = - \frac{1}{2}, y = - \frac{1}{2}$
3. $x = \frac{1}{2}, y = - \frac{1}{2}$
4. $x = - \frac{1}{2}, y = \frac{1}{2}$

26.

The quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of
1. Pressure
2. Work
3. Latent heat
4. None of the above

27.

An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle?
(1) $M L T^{- 2}$
(2) $M L^{2} T^{- 2}$
(3) MLT²
(4) L

28.

Dimensions of strain are:
(1) $M L T^{- 1}$
(2) $M L^{2} T^{- 1}$
(3) $M L T^{- 2}$
(4) $M^{0} L^{0} T^{0}$

29.

If $97.52$ is divided by $2.54$, the correct result in terms of significant figures is:

1.	$ 38.4 $	2.	$38.3937 $
3.	$ 38.394 $	4.	$38.39$

30.

Assertion : Radian is the unit of plane angle.
Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

31.

The unit of permittivity of free space $ε_{0}$ is
(1) Coulomb/Newton-metre
(2) Newton-metre²/Coulomb²
(3) Coulomb²/(Newton-metre)²
(4) Coulomb²/Newton-metre²

32.

The position of a particle at time t is given by the relation $l = \frac{v_{o}}{α} (1 - e^{α t})$ , where v₀ is a constant and α > 0. The dimensions of v₀ and α are respectively
(1) $M^{0} L^{1} T^{- 1}$ and T^–1
(2) $M^{0} L^{1} T^{0}$ and T^–1
(3) $M^{0} L^{1} T^{- 1}$ and LT^–2
(4) $M^{0} L^{1} T^{- 1}$ and T

33.

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be
(1) $3 + 6 .01 \times \frac{100}{5 .3}$
(2) $\frac{1}{3} \times 0 .01 \times \frac{100}{5 .3}$
(3) $(\frac{3 \times 0 .1}{5 .3}) \times 100$
(4) $\frac{0 .1}{5 .3} \times 100$

34.

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%. The maximum error in the measurement of pressure is
(1) 1%
(2) 2%
(3) 6%
(4) 8%

35.

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation $g = 4 π^{2} (l / T^{2})$ will be
(1) 2%
(2) 4%
(3) 7%
(4) 10%

36.

Two full turns of the circular scale of gauge cover a distance of $1$ mm on scale. The total number of divisions on the circular scale is $50.$ Further, it is found that screw gauge has a zero error of $-0.03$ mm. While measuring the diameter of a thin wire a student notes the main scale reading of $3$ mm and the number of circular scale division in line, with the main scale as $35.$ The diameter of the wire is:
1. $3.32$ mm
2. $3.73$ mm
3. $3.67$ mm
4. $3.38$ mm

37.

The circular division of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is

(1) 2.25 mm
(2) 2.20 mm
(3) 1.20 mm
(4) 1.25 mm

38.

One cm on the main scale of vernier callipers is divided into ten equal parts. If 20 divisions of vernier scale coincide with 8 small divisions of the main scale. What will be the least count of callipers?
1. 0.06 cm
2. 0.6 cm
3. 0.5 cm
4. 0.7 cm

39.

Find the zero correction in the given figure.

1. 0.4 mm
2. 0.5 mm
3. -0.5 mm
4. -0.4 mm

40.

The dimensions of universal gravitational constant are
(1) $[M L^{2} T^{- 1}]$
(2) $[M^{- 2} L^{3} T^{- 2}]$
(3) $[M^{- 2} L^{2} T^{- 1}]$
(4) $[M^{- 1} L^{3} T^{- 2}]$

41.

The velocity $ν$ of a particle at time t is given by $ν = a t + \frac{b}{t + c}$ , where a, b, and c are constants. The dimensions of a, b and c are respectively.
(1) $L T^{- 2}, L a n d T$
(2) $L^{2}, T a n d L T^{2}$
(3) $L T^{2}, L T a n d L$
(4) $L, L T a n d T^{2}$

42.

If the dimensions of a physical quantity are given by $[M^{a} L^{b} T^{c}]$ , then the physical quantity will be
(1) velocity if a = 1, b = 0, c = -1
(2) acceleration if a = 1, b = 1, c = -2
(3) force if a = 0, b = -1, c = -2
(4) Pressure if a = 1, b =-1, c = -2

43.

A student measures the distance traversed in the free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_{1} a n d e_{2}$ , respectively, the percentage error in the estimation of g is
(1) $e_{1} + 2 e_{2}$
(2) $e_{1} + e_{2}$
(3) $e_{1} - 2 e_{2}$
(4) $e_{2} - e_{1}$

44.

In an experiment four quantities a , b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as $P = \frac{a^{3} b^{2}}{c d}$ . % error in P is
(1) 14%
(2) 10%
(3) 7%
(4) 4%

45.

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is
(1) 0.053 cm
(2) 0.525 cm
(3) 0.521 cm
(4) 0.529 cm

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1.	\(n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)
2.	\(n_1u_1+n_2u_2=0\)
3.	\(n_1n_2=u_1u_2\)
4.	\((n_1+u_1)=(n_2+u_2)\)

1.	\( 38.4 \)	2.	\(38.3937 \)
3.	\( 38.394 \)	4.	\(38.39\)

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