The relation amongst the three elements of Earth's magnetic field, namely horizontal component H, vertical component V and dip angle is: (=total magnetic field):
1. V=tan, H=
2. V=sin, H=cos
3. V=cos, H=sin
4. V=, H=tan
A proton and an \(\alpha\text{-}\)particle are accelerated from rest to the same energy. The de-Broglie wavelength \(\lambda_p\) and \(\lambda_\alpha\) are in the ratio:
1. \(2:1\)
2. \(1:1\)
3. \(\sqrt{2}:1\)
4. \(4:1\)
A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of \(a.\) In the frame of the truck, the pendulum will tilt:
| 1. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{sin}^{-1} \left( \dfrac{a}{g} \right )\) |
| 2. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{cos}^{-1} \left ( \dfrac{a}{g} \right )\) |
| 3. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{a}{g} \right )\) |
| 4. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{g}{a} \right )\) |
| 1. | \(6\sqrt{2}~\text{hr}\) | 2. | \(12\sqrt{2}~\text{hr}\) |
| 3. | \(\frac{24}{2.5}~\text{hr}\) | 4. | \(\frac{12}{2.5}~\text{hr}\) |
1. \(\sigma_{1}=\dfrac{5}{6}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
2. \(\sigma_{1}=\dfrac{5}{2}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
3. \(\sigma_{1}=\dfrac{5}{2}\sigma ,~\sigma_{2}=\dfrac{5}{3}\sigma\)
4. \(\sigma_{1}=\dfrac{5}{3}\sigma ,~\sigma_{2}=\dfrac{5}{6}\sigma\)
Two identical capacitors \(C_{1}\) and \(C_{2}\) of equal capacitance are connected as shown in the circuit. Terminals \(a\) and \(b\) of the key \(k\) are connected to charge capacitor \(C_{1}\) using a battery of emf \(V\) volt. Now disconnecting \(a\) and \(b\) terminals, terminals \(b\) and \(c\) are connected. Due to this, what will be the percentage loss of energy?
| 1. | \(75\%\) | 2. | \(0\%\) |
| 3. | \(50\%\) | 4. | \(25\%\) |
The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
| 1. | \(\dfrac{1}{(n+1)(n-1)}\) cm | 2. | \(\dfrac{1}{n}\) cm |
| 3. | \(\dfrac{1}{n^{2}}\) cm | 4. | \(\dfrac{1}{(n)(n+1)}\) cm |
A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}~\text C.\) What is the total electric flux through the sphere?
1. \(-3\times10^{-6}~\text{N-m}^2/\text C\)
2. zero
3. \(3\times10^{-6}~\text{N-m}^2/\text C\)
4. \(6\times10^{-6}~\text{N-m}^2/\text C\)
The work function of the photosensitive material is \(4.0~\text{eV}\). The longest wavelength of light that can cause photoelectric emission from the substance is (approximately):
1. \(3100~\text{nm}\)
2. \(966~\text{nm}\)
3. \(31~\text{nm}\)
4. \(310~\text{nm}\)
A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction = \(\mu).\) A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec {F}\) where:
1. \(|{\vec {F}}| = mg+\mu mg\)
2. \(|\vec {F}| =\mu mg\)
3. \(|\vec {F}| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec{F}| = mg\)
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