The velocity velocity vector v and displacement vector x of a particle executing SHM are related as 
 with the initial condition  at x = 0. The velocity v, when displacement is x, is

1. $v= \sqrt{v_0^2+{\omega }^2{x}^2}$

2. $v= \sqrt{v_0^2-{\omega }^2{x}^2}$

3. $v=\sqrt[3]{v_0^2+{\omega }^2{x}^2}$

4. $v=v_0-({\omega }^3{x}^3{e}^{x^3}{)}^{1/3}$

Consider the diagram shown below in which two masses of m and 2m are placed on a fixed triangular wedge. 
 
The coefficient of friction between block A and the wedge is 2/3, while that for block B and the wedge is 1/3. 
If the whole system is released from rest, then acceleration of block A is

1. Zero

2. $\frac{2 m^2}{3}g$

3. $\frac{4 m^2}{3}$g

4. $\frac{m^2}{\sqrt{2}}g$

In the arrangement shown in figure, the current through 5 Ω resistor is 

1. 2 A

2. zero

3. $\frac{12}{7}$A

4. 1 A

A hemispherical bowl of radius r is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is θ, then find the angular speed at which the ball is rotating.

1. $\omega =\sqrt{rg \sin \theta }$

2. \(\omega= \sqrt{\frac{g}{rcos\theta }}\)

3. $\omega =\sqrt{\frac{gr}{\cos \theta }}$

4. $\omega =\sqrt{\frac{gr}{\tan \theta }}$

The phase difference between the flux linked with a ball rotating in a uniform magnetic field and induced emf produced in it is

$1. \mathrm{\pi }/2$
$$
$2. \mathrm{\pi }/3$
$$
$3. -\mathrm{\pi }/6$
$$
$4. \mathrm{\pi }$

A condenser of 250 is connected in parallel to a coil of inductance of 0.16 mH, while its effective resistance is 20 Ω. Determine the resonant frequency.

1. $9\times {10}^{4}Hz$

2. $16\times {10}^{7}Hz$

3. $8\times {10}^{5}Hz$

4. $9\times {10}^{3}Hz$

For Bragg’s diffraction by a crystal to occur, then the X-ray of wavelength and interatomic distance d must be

1. $\lambda$ is greater than 2d

2. $\lambda$ equals 2d

3. $\lambda$ is smaller than or equal to 2d

4. $\lambda$ is smaller than 2d

A wire having mass m and length l can freely slide on a pair of parallel smooth horizontal rails placed in vertical magnetic field B. The rails are connected by a capacitor of capacitance C. The electric resistance of the rails and the wire as shown in the figure. Then, the acceleration of the wire can be given as 

1. $a=\frac{C^2{B}^2 l-F}{m}$

2. $a=\frac{F}{m+CBl}$

3. $a=\frac{F{C}^2{B}^2 l}{m}$

4. $a=\frac{F}{m+C^2{B}^{2}l}$

Consider the situation shown in figure A spring of spring constant 400 N/m is attached at one end to a wedge fixed rigidly with the horizontal part. A 40 g mass is released form rest while situated at a height 5 cm the curved track. The minimum deformation in the spring is nearly equal to  

1. 9.8 m

2. 9.8 cm

3. 0.98 m

4. 0.009 km