Q. No.Two springs, of force constants k1 and k2 are connected to a mass m as shown in the figure. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation will become:
1.
2f
2.
f/2
3.
f/4
4.
4f
1. \(24~\text{J}\)
2. \(36~\text{J}\)
3. \(16~\text{J}\)
4. \(20~\text{J}\)
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
A block of mass \(4~\text{kg}\) hangs from a spring of spring constant \(k = 400~\text{N/m}\). The block is pulled down through \(15~\text{cm}\) below the equilibrium position and released. What is its kinetic energy when the block is \(10~\text{cm}\) below the equilibrium position? [Ignore gravity]
1. \(5~\text{J}\)
2. \(2.5~\text{J}\)
3. \(1~\text{J}\)
4. \(1.9~\text{J}\)
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
| 1. | Spring constant | 2. | Angular frequency |
| 3. | (Angular frequency)2 | 4. | Restoring force |
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
1. \(0~\text{and}~2K_0\)
2. \(\frac{K_0}{2}~\text{and}~K_0\)
3. \(K_0~\text{and}~2K_0\)
4. \(K_0~\text{and}~K_0\)
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