When the circular scale of a screw gauge completes \(2\) rotations, it covers \(1\) mm over the pitch scale. The total number of circular scale divisions is \(50\). The least count of the screw gauge in metres is:
1. \(10^{-4}\)
2. \(10^{-5}\)
3. \(10^{-2}\)
4. \(10^{-3}\)
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. | \(u\sqrt{\dfrac{m}{k}}\) | 2. | \(4u\sqrt{\dfrac{m}{k}}\) |
3. | \(2u\sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
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. | \(\dfrac{13q}{4\pi \varepsilon_0r^2}\) | 2. | zero |
3. | \(\dfrac{q}{4\pi \varepsilon_0r^2}\) | 4. | \(\dfrac{12q}{4\pi \varepsilon_0r^2}\) |
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. \(\text{OR}\) gate
2. \(\text{NOR}\) gate
3. \(\text{AND}\) gate
4. \(\text{NAND}\) gate
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 of \(10\) N, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2\) s will be:
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. | \(\text{tan}^{-1}\Big(\dfrac{12}{37}\Big)\) with respect to rain |
2. | \(\text{tan}^{-1}\Big(\dfrac{12}{37}\Big)\) with respect to wind |
3. | \(\text{tan}^{-1}\Big(\dfrac{12}{35}\Big)\) with respect to rain |
4. | \(\text{tan}^{-1}\Big(\dfrac{12}{35}\Big)\) with respect to wind |