Q. No.A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))
1.
\(10\) s and \(99\) m/s
2.
\(10\) s and \(15\) m/s
3.
\(5\) s and \(99\) m/s
4.
\(5\) s and \(15\) m/s
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:
1. \(2.5\) s
2. \(2.9\) s
3. \(3.5\) s
4. \(3\) s
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?
| 1. | \(0.62\) rad/s | 2. | \(0.06\) rad/s |
| 3. | \(4.40\) rad/s | 4. | \(0.44\) rad/s |
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?
1. \(\text{yes},\) \(2.3~\text{cm/s}^2\)
2. \(\text{no},\) \(5.3~\text{cm/s}^2\)
3. \(\text{yes},\) \(5.3~\text{cm/s}^2\)
4. \(\text{no},\) \(2.3~\text{cm/s}^2\)
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^{\circ}\) above the horizontal. The maximum height attained by the ball is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m
A car starts from rest and accelerates at \(5~\text{m/s}^{2}.\) At \(t=4~\text{s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t=6~\text{s}?\)
(Take \(g=10~\text{m/s}^2\))
1. \(20\sqrt{2}~\text{m/s}, 0~\text{m/s}^2\)
2. \(20\sqrt{2}~\text{m/s}, 10~\text{m/s}^2\)
3. \(20~\text{m/s}, 5~\text{m/s}^2\)
4. \(20~\text{m/s}, 0~\text{m/s}^2\)
| 1. | \( \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\) | 2. | \(\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) |
| 3. | \(\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) | 4. | \(\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:
| 1. | are equal to each other. |
| 2. | are not equal to each other. |
| 3. | are sometimes equal and sometimes not equal to each other. |
| 4. | depends on the difference between the angles. |
Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?
| 1. | in the vertical direction only. |
| 2. | \(19^\circ\) with vertical towards east. |
| 3. | \(19^\circ\) with vertical towards the west. |
| 4. | \(19^\circ\) with vertical towards the south. |
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0 \hat j)~\text{m/s}^2\). What is the y-coordinate of the particle at the instant its \(x\text-\)coordinate is \(84\) m?
1. \(36\) m
2. \(26\) m
3. \(1\) m
4. \(0\) m
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