A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
1.
\(u\sqrt{\frac{m}{k}}\)
2.
\(4u\sqrt{\frac{m}{k}}\)
3.
\(2u\sqrt{\frac{m}{k}}\)
4.
\(\frac12u\sqrt{\frac{k}{m}}\)
(The friction between the block and the surface is negligible).
If \(\lambda_X,\lambda_I,\lambda_M\) and \(\lambda_\gamma\) are the wavelengths of \(X\)-rays, infrared rays, microwaves and \(\gamma\)-rays respectively, then:
| 1. | \(\lambda_\gamma<\lambda_X<\lambda_I<\lambda_M\) |
| 2. | \(\lambda_M<\lambda_I<\lambda_X<\lambda_\gamma\) |
| 3. | \(\lambda_X<\lambda_\gamma<\lambda_M<\lambda_I\) |
| 4. | \(\lambda_X<\lambda_I<\lambda_\gamma<\lambda_M\) |
Twelve point charges each of charge \(q\) C are placed at the circumference of a circle of radius \(r\) m with equal angular spacing. If one of the charges is removed, the net electric field (in N/C) at the centre of the circle is:
(\(\varepsilon_0 \)-permittivity of free space)
1. \(\frac{13q}{4\pi \varepsilon_0r^2}\)
2. zero
3. \(\frac{q}{4\pi \varepsilon_0r^2}\)
4. \(\frac{12q}{4\pi \varepsilon_0r^2}\)
Let \(L_1\) and \(L_2\) be the orbital angular momentum of an electron in the first and second excited states of the hydrogen atom, respectively. According to Bohr's model, the ratio \(L_1:L_2\) is:
1. \(1:2\)
2. \(2:1\)
3. \(3:2\)
4. \(2:3\)
The output of the logic circuit shown is equivalent to a/an:
1. \(\mathrm{OR}\) gate
2. \(\mathrm{NOR}\) gate
3. \(\mathrm{AND}\) gate
4. \(\mathrm{NAND}\) gate
A strong magnetic field is applied along the direction of the velocity of an electron. The electron would move along:
| 1. | a parabolic path |
| 2. | the original path |
| 3. | a helical path |
| 4. | a circular path |
A string is wrapped along the rim of a wheel of moment of inertia \(0.10\) kg-m2 and radius \(10\) cm. If the string is now pulled by a force \(10\) N, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2\) seconds is:
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s
A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (Take \(g=10\) m/s2)
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m
Rain is falling vertically downward with a speed of \(35~\text{m/s}\). Wind starts blowing after some time with a speed of \(12~\text{m/s}\) in East to West direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
An electromagnetic wave is moving along negative \(\text{z (-z)}\) direction and at any instant of time, at a point, its electric field vector is \(3\hat j~\text{V/m}\). The corresponding magnetic field at that point and instant will be: (Take \(c=3\times10^{8}~\text{ms}^{-1}\) )
| 1. | \(10\hat i~\text{nT}\) | 2. | \(-10\hat i~\text{nT}\) |
| 3. | \(\hat i~\text{nT}\) | 4. | \(-\hat i~\text{nT}\) |
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