A particle of mass \(1\) mg has the same wavelength as an electron moving with a velocity of  \(3\times 10^{6}\) ms^-1. The velocity of the particle is:
(Mass of electron = \(9.1 \times 10^{-31}\) kg)
1. \(2.7 \times 10^{-18}~\text{ms}^{-1}\)
2. \(9 \times 10^{-2}~\text{ms}^{-1}\)
3. \(3 \times 10^{-31}~\text{ms}^{-1}\)
4. \(2.7 \times 10^{-21}~\text{ms}^{-1}\)

A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

                                 

A cell can be balanced against 100 cm and 110 cm of potentiometer wire, respectively with and without being short-circuited through a resistance of 10 Ω. Its internal resistance is:

1.  1.0 Ω

2.  0.5 Ω

3.  2.0 Ω

4.  zero

If \(M(A,~Z)\), \(M_p\)${}_{}$, and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) \((1~u=931.5~\text{MeV/c}^2)\) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is:
                 

1.  $0.5$ $\mathrm{N}$

2.  $1.5$ $\mathrm{N}$

3.  $\frac{\sqrt{3}}{4}$ $\mathrm{N}$

4.  $\sqrt{3}$ $\mathrm{N}$

Two periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

1.  $2\left({\mathrm{l}}_1+{\mathrm{l}}_2\right)$

2.  ${\left({\sqrt{\mathrm{I}}}_1+{\sqrt{\mathrm{l}}}_2\right)}^2$

3.  ${\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)}^2$

4.  $2\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)$

A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:

1. 100 ms^-1

2. 80 ms^-1

3. 40 ms^-1

4. 120 ms^-1