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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

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. \(\text{dyne} / \text{cm}^2\)

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. $x=-\frac{1}{2},y=\frac{1}{2}$

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 $\lambda$, the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as: 
1. ${\mathrm{v}}^2\propto {\mathrm{g\lambda }}^{-1}{\mathrm{\rho }}^{-1}$
2. ${\mathrm{v}}^2\propto \mathrm{g\lambda \rho }$
3. ${\mathrm{v}}^2\propto \mathrm{g\lambda }$
4. ${\mathrm{v}}^2\propto {\mathrm{g}}^{-1}{\mathrm{\lambda }}^{-3}$

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on (i) the mass of the ball m, (ii) $\eta$, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?
1. $v_T\propto \frac{mg}{\eta r}$
2. $v_T\propto \frac{\eta r}{mg}$
3. $v_T\propto \eta rmg$
4. $v_T\propto \frac{mgr}{\eta }$ 

The quantity $X=\frac{{\epsilon }_{0}LV}{t}; {\epsilon }_0$ 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 period of oscillation of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$ where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stopwatch of least count 0.1 s. The percentage error in g is:
1. 0.1%
2. 1%
3. 0.2%
4. 0.8%

A body travels uniformly a distance of (13.8 $\pm$ 0.2) m in a time (4.0 ± 0.3) sec. The velocity of the body within error limits is:
1. (3.45 ± 0.2) ms^-1
2. (3.45 ± 0.3) ms^-1
3. (3.45 ± 0.4) ms^-1
4. (3.45 ± 0.5) ms^-1

In the context of the accuracy of measurement and significant figures in expressing the results of the experiment, which of the following is/are correct?
(1) Out of the two measurements 50.14 cm and 0.00025 Amperes, the first one has greater accuracy.
(2) If one travels 478 km by rail and 397 m by road, the total distance traveled is 478 km.
1. Only (1) is correct
2. Only (2) is correct
3. Both are correct
4. None of them is correct.

The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00 ± 0.05) Newton and weight in water is (4.00 ± 0.05) Newton. Then the relative density along with the maximum permissible percentage error is
1. 5.0 ± 11%
2. 5.0 ± 1%
3. 5.0 ± 6%
4. 1.25 ± 5%

If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [$\eta$^xρ^yr^z]  , where $\eta$, 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

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 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