A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:
| 1. | \(\sqrt{\dfrac{Rg}{\mu_s} }\) | 2. | \(\sqrt{\dfrac{mRg}{\mu_s}}\) |
| 3. | \(\sqrt{\mu_s Rg}\) | 4. | \(\sqrt{\mu_s m Rg}\) |
A circular platform is mounted on a frictionless vertical axle. Its radius \(R = 2~\text{m}\) and its moment of inertia about the axle is \(200~\text{kg m}^2\). It is initially at rest. A \(50~\text{kg}\) man stands on the edge of the platform and begins to walk along the edge at the speed of \(1~\text{ms}^{-1}\) relative to the ground. The time taken by man to complete one revolution is:
| 1. | \(\dfrac{3\pi}{2}\text{s}\) | 2. | \(2\pi~\text{s}\) |
| 3. | \(\dfrac{\pi}{2}\text{s}\) | 4. | \(\pi~\text{s}\) |
If the momentum of an electron is changed by \(p,\) then the de-Broglie wavelength associated with it changes by \(0.5\%.\) The initial momentum of an electron will be:
| 1. | \(400p\) | 2. | \(\frac{p}{100}\) |
| 3. | \(100p\) | 4. | \(200p\) |
| 1. | \(v_o=v_e\) | 2. | \(v_e=\sqrt{2v_o}\) |
| 3. | \(v_e=\sqrt{2}~v_o\) | 4. | \(v_o=\sqrt{2}~v_e\) |
The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:
| 1. | \(\frac{3\pi}{2}\) | 2. | \(3\pi\) |
| 3. | \(\frac{2\pi}{3}\) | 4. | \(2\pi\) |
A proton carrying \(1~\text{MeV}\) kinetic energy is moving in a circular path of radius \(R\) in a uniform magnetic field. What should be the energy of an \(\alpha \text- \)particle to describe a circle of the same radius in the same field?
| 1. | \(1~\text{MeV}\) | 2. | \(0.5~\text{MeV}\) |
| 3. | \(4~\text{MeV}\) | 4. | \(2~\text{MeV}\) |
Three masses are placed on the \(x\)-axis: \(300~\text{g}\) at origin, \(500~\text{g}\) at \(x= 40~\text{cm}\) and \(400~\text{g}\) at \(x= 70~\text{cm}.\) The distance of the centre of mass from the origin is:
1. \(45~\text{cm}\)
2. \(50~\text{cm}\)
3. \(30~\text{cm}\)
4. \(40~\text{cm}\)
In a coil of resistance \(10\) \(\Omega\), the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:
| 1. | \(2\) | 2. | \(6\) |
| 3. | \(4\) | 4. | \(8\) |
A parallel plate capacitor has a uniform electric field \(E\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A,\) the energy stored in the capacitor is:
| 1. | \(\dfrac{E^2 Ad}{\varepsilon_0}\) | 2. | \(\dfrac{1}{2}\varepsilon_0E^2 Ad\) |
| 3. | \(\varepsilon_0EAd\) | 4. | \(\dfrac{1}{2}\varepsilon_0E^2 \) |
A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
| 1. | \(t^{\frac{1}{2}}\) | 2. | \(t^{\frac{-1}{2}}\) |
| 3. | \(\frac{t}{\sqrt{m}}\) | 4. | \(t^2 P_0\) |
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