In \(S= a+bt+ct^2,~S\) is measured in metres and \(t\) in seconds. The unit of \(c\) will be:
1. | none | 2. | \(\text{m}\) |
3. | \(\text{ms}^{-1}\) | 4. | \(\text{ms}^{-2}\) |
The velocity of a particle depends upon as ; if the velocity is in , the unit of a will be
(1)
(2)
(3)
(4)
If , 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)
(2)
(3)
(4)
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. \(\text{dyne} / \text{cm}^2\)
A spherical body of mass m and radius r is allowed to fall in a medium of viscosity . The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity is called time constant . Dimensionally can be represented by
(1)
(b)
(c)
(4) None of the above
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 ; where C is a dimensionless quantity. The value of x and y are
1.
2.
3.
4.
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
The velocity of water waves v may depend upon their wavelength , the density of water and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as:
1.
2.
3.
4.
The equation of a wave is given by where is the angular velocity, x is length and is the linear velocity. The dimension of k is
(1) LT
(2) T
(3)
(4) T2
The period of a body under SHM is presented by ; where P is pressure, D is density and S is surface tension. The value of a, b and c are:
1.
2.
3.
4.
The velocity of a freely falling body changes according to where g is acceleration due to gravity and h is the height. The values of p and q are:
(1)
(2)
(3)
(4) 1, 1
A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity . After some time the velocity of the ball attains a constant value known as terminal velocity . The terminal velocity depends on (i) the mass of the ball m, (ii) , (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?
1.
2.
3.
4.
The quantity is the permittivity of free space, L is length, V is the potential difference and t is time. The dimensions of X are the same as that of:
1. Resistance
2. Charge
3. Voltage
4. Current
The dimensions of physical quantity X in the equation Force is given by
(1)
(2)
(3)
(4)
If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that is dimensionless, are
(1)
(2)
(3)
(4)
Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful?
(1) A/B
(2) A + B
(3) A – B
(4) None
Given that v is speed, r is the radius and g is the acceleration due to gravity. Which of the following is dimensionless?
(1)
(2)
(3)
(4)
A force F is given by F = at + bt2, where t is time. What are the dimensions of a and b:
(1) and
(2) and
(3) and
(4) and
If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is
(1)
(2)
(3)
(4)
If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density of the liquid, then the expression of T is
(1)
(2)
(3)
(4) None of these
If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is
(1)
(2)
(3)
(4)
A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be:
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)
The position of a particle at time t is given by the relation , where v0 is a constant and α > 0. The dimensions of v0 and α are respectively
(1) and T–1
(2) and T–1
(3) and LT–2
(4) and T
If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be
(1)
(2)
(3)
(4)
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%
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 will be
(1) 2%
(2) 4%
(3) 7%
(4) 10%
If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [xρyrz] , where , ρ and r are the coefficient of viscosity of the liquid, the 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
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 follows P=a3b2/cd %, Error in P is
1. 14%
2. 10%
3. 7%
4. 4%
A student measures the distance traversed in 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 and respectively, the percentage error in the estimation of g is
1.
2.
3.
4.
If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:
1. 4% 2. 6%
3. 8% 4. 2%
The pitch of a screw gauge is 1.0 mm and there are 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 mm and the 47th division on the circular scale coincides with the reference line. The length of the wire is 5.6 cm. Find the wire's curved surface area (in cm2) in an appropriate number of significant figures.
1. 2.4 cm2
2. 2.56 cm2
3. 2.6 cm2
4. 2.8 cm2
Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?
It is given that the circular head translates \(\mathrm{P}\) MSD in \(\mathrm{N}\) rotations. (\(1\) MSD \(=\) \(\mathrm{1~mm}\).)
1. \( \left(\frac{\mathrm{P}}{\mathrm{N}}\right)\left(2+\frac{45}{100}\right) \mathrm{mm} \)
2. \( \left(\frac{\mathrm{N}}{\mathrm{P}}\right)\left(2+\frac{45}{\mathrm{~N}}\right) \mathrm{mm} \)
3. \( \mathrm{P}\left(\frac{2}{\mathrm{~N}}+\frac{45}{100}\right) \mathrm{mm} \)
4. \( \left(2+\frac{45}{100} \times \frac{\mathrm{P}}{\mathrm{N}}\right) \mathrm{mm}\)
A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument? 1 msd = 100 csd = 1 mm
1. | -0.16 mm | 2. | +0.16 mm |
3. | +0.14 mm | 4. | -0.14 mm |
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
Find the zero correction in the given figure.
1. 0.4 mm
2. 0.5 mm
3. -0.5 mm
4. -0.4 mm
Find the zero correction in the given figure.
1. -0.6 mm
2. +0.6 mm
3. 0.4 mm
4. - 0.4 mm
Find the thickness of the wire. The least count is 0.01 mm. The main scale reads in mm.
1. 7.62 mm
2. 7.63 mm
3. 7.64 mm
4. 7.65 mm
The main scale reading is \(-1\) mm when there is no object between the jaws. In the vernier calipers, \(9\) main scale division matches with \(10\) vernier scale divisions. Assume the edge of the Vernier scale as the '0' of the vernier. The thickness of the object using the defected vernier calipers will be:
1. \(12.2~\text{mm}\)
2. \(1.22~\text{mm}\)
3. \(12.3~\text{mm}\)
4. \(12.4~\text{mm}\)
Read the special type of vernier. 20 division of vernier scale are matching with 19 divisions of main scale. Find the reading of the instrument. Assume edge of vernier as '0' of vernier and No Zero error
(1) 13.70 mm
(2) 13.60 mm
(3) 1.36 mm
(4) 1.37 mm
In the vernier callipers given below, 9 main scale divisions matched with 10 vernier scale divisions. Assume the edge of the vernier scale as the '0' for the vernier scale. The thickness of the object using the defective vernier callipers will be:
1. 13.3 mm
2. 13.4 mm
3. 13.5 mm
4. 13.6 mm
In the vernier calipers, 9 main scale divisions match with 10 vernier scale division. First figure shows the zero error. Assume the edge of vernier as the '0' of vernier. The thickness of the object using the defected vernier callipers will be:
(1) 14.0 mm
(2) 1.40 mm
(3) -14.0 mm
(4) -1.40 mm
The main scale of a vernier callipers reads 10 mm in 10 divisions. 10 divisions of Vernier scale coincide with 9 divisions of the main scale. When the two jaws of the callipers touch each other, the fifth division of the vernier coincides with 9 main scale divisions and the zero of the vernier is to the right of zero of main scale. When a cylinder is tightly placed between the two jaws, the zero of vernier scale lies slightly behind 3.2 cm and the fourth vernier division coincides with a main scale division. The diameter of the cylinder is.
(1) 3.10 cm
(2) 3.8 cm
(3) 3.09 cm
(4) -3.09 cm
If z=, and errors in the determination of A and B are respectively , then the fractional error in the calculation of z is :
Two resistors are connected in parallel. The equivalent resistance is :