The dimensional formula of the coefficient of thermal conductivity is :
1.
2.
3.
4.
The measurements are made as 18.425 cm, 7.21 cm, and 5.0 cm. The addition of these measurements should be written as:
1. 30.635 cm
2. 30.64 cm
3. 30.63 cm
4. 30.6 cm
A physical parameter '\(a\)' can be determined by measuring the parameters \(b\), and using the relation\(,a= \frac{b^{\alpha}c^{\beta}}{d^{\gamma}e^{\delta}}.\) If the maximum errors in the measurement of \(b, ~c, ~d,~\text{and}~e\) are \(b_1\%,~c_1\%,~d_1\%~\text{and}~e_1\%\)
1. \((b_1+c_1+d_1+e_1)\%\)
2. \((b_1+c_1-d_1-e_1)\%\)
3. \(\alpha b_1+\beta c_1-\gamma d_1-\delta e_1\%\)
4. \(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1\%\)
The unit of angular acceleration in the SI system is
(1)
(2)
(3)
(4)
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.