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Q. No.A ball \((A)\) is projected vertically upward, a second ball \((B)\) is projected horizontally with the same initial speed as the first. The relative velocity of ball \(A\) with respect to \(B\):
| 1. | is constant in magnitude only. |
| 2. | is constant in direction. |
| 3. | is constant in magnitude and direction. |
| 4. | varies, both, in magnitude and direction. |
Subtopic: Relative Motion in One Dimension |
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Two cars \(A\) and \(B\) start moving along the same straight road, from the same point, simultaneously. The first car \((A)\) accelerates uniformly to a maximum speed of \(v_0\) and then decelerates uniformly to a stop. The second car \((B)\) accelerates uniformly to the same maximum speed \(v_0\) and then decelerates uniformly to a stop. The acceleration of \(A\) is twice that of \(B,\) and they both spend the same total time during the motion. Then,
Choose the correct option from the given ones:
| (A) | distance travelled by \(A\) = distance travelled by \(B\) |
| (B) | acceleration time of \(A\) = \(\dfrac12\) acceleration time of \(B\) |
| (C) | relative velocity of \(A\) with respect to \(B\) is always positive |
| (D) | deceleration time of \(A\) = \(2×\) deceleration time of \(B\) |
Choose the correct option from the given ones:
| 1. | (A) is True. |
| 2. | (A), (B) are True. |
| 3. | (A), (B), (C) are True. |
| 4. | (B), (C), (D) are True. |
Subtopic: Acceleration |
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The line \(AB\) makes a \(45^\circ\) angle with the \(x\)-axis, but it moves along the negative \(y\)-axis with a speed of \(1~\text{m/s}.\) The velocity, of the intersection \((C)\) of \(AB\) with \(x\)-axis, is:
| 1. | \(1~\text{m/s}\) along the positive \(x\)-axis |
| 2. | \(1~\text{m/s}\) along the negative \(x\)-axis |
| 3. | \(\dfrac{1}{\sqrt2} ~\text{m/s}\) along the positive \(x\)-axis |
| 4. | \(\dfrac{1}{\sqrt2}~\text{m/s}\) along the negative \(x\)-axis |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
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A man driving a scooter at \(15~\text{m/s}\) brakes at the rate of \(2~\text{m/s}^2\). His speed, after \(10~\text{s}\) after the application of brakes will be:
1. \(5~\text{m/s}\)
2. \(-5~\text{m/s}\)
3. \(0~\text{m/s}\)
4. \(10~\text{m/s}\)
Subtopic: Uniformly Accelerated Motion |
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Two cars \(A\) and \(B,\) each \(5~\text{m}\) long, are travelling along parallel lanes with speeds of \(36~\text{km/hr}\) and \(72~\text{km/hr}.\) The car \(B\) is just behind the car \(A,\) but is beginning to overtake. What will be the distance covered by the car \(B\) by the time it is just ahead of the car \(A?\)
| 1. | \(10~\text{m}\) | 2. | \(15~\text{m}\) |
| 3. | \(20~\text{m}\) | 4. | \(25~\text{m}\) |
Subtopic: Relative Motion in One Dimension |
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A boy throws a ball straight up the side of a building and receives it after \(4\) s. On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3\) s. The ledge is at a distance \(d\) below the highest point, where \(d=?\) (take acceleration due to gravity, \(g=10\) m/s2)
1. \(5\) m
2. \(2.5\) m
3. \(1.25\) m
4. \(10\) m
Subtopic: Distance & Displacement |
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The velocity-time graph of a particle moving along a straight line is shown in the adjacent figure. The average velocity is:
| 1. | \(1\) m/s |
| 2. | \(2\) m/s |
| 3. | less than \(1\) m/s |
| 4. | greater than \(2\) m/s |
Subtopic: Graphs |
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A balloon ascends upward with a constant upward velocity \(5\) m/s. At the same time it is being pushed to the right by the wind with a speed that is proportional to its height \((y)\): \(v_\text{right}=2y\)
where the units are in SI. The acceleration of the balloon is:
1. zero
2. \(10\) m/s2 to right
3. \(5\) m/s2 to right
4. \(10\) m/s2 upward
where the units are in SI. The acceleration of the balloon is:
1. zero
2. \(10\) m/s2 to right
3. \(5\) m/s2 to right
4. \(10\) m/s2 upward
Subtopic: Acceleration |
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A particle is projected vertically upwards with a speed \(u\) and moves under the force of gravity. The distance travelled by the particle during its entire motion (until it returns) is \(d_1.\) If the force of gravity were to be switched off, and the particle travelled for the same length of time, then the distance travelled is \(d_2.\) Then,
1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\)
4. \(d_2 = 4 d_1\)
1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\)
4. \(d_2 = 4 d_1\)
Subtopic: Uniformly Accelerated Motion |
53%
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Two particles, \(A\) & \(B,\) move along the \(x\)-axis (as shown in the figure) with their initial velocities \(u_{\Large_A},u_{\Large_B}\) and their accelerations \(a_{\Large_A},a_{\Large_B}\) (constant accelerations). Their relative separation \(s\) is measured from \(A\) towards \(B,\) with the initial condition as depicted in the figure. Match the conditions mentioned in column I with the corresponding correct graph of \(s,\) in column II.
| Column I | Column II | ||
| \(\mathrm{(A)}\) | \(a_{\Large_A}=a_{\Large_B}\neq 0\) | \(\mathrm{(I)}\) |  |
| \(\mathrm{(B)}\) | \(a_{\Large_A}>a_{\Large_B},u_{\Large_A}<u_{\Large_B}\) | \(\mathrm{(II)}\) |  |
| \(\mathrm{(C)}\) | \(a_{\Large_A}<a_{\Large_B},u_{\Large_A}=u_{\Large_B}\) | \(\mathrm{(III)}\) |  |
| \(\mathrm{(D)}\) | \(a_{\Large_A}<a_{\Large_B},u_{\Large_A}<u_{\Large_B}\) | \(\mathrm{(IV)}\) |  |
| 1. | \(\mathrm{A\text-II,B\text-I,C\text-IV,D\text-III}\) | 2. | \(\mathrm{A\text-III,B\text-IV,C\text-II,D\text-I}\) |
| 3. | \(\mathrm{A\text-II,B\text-IV,C\text-III,D\text-I}\) | 4. | \(\mathrm{A\text-III,B\text-I,C\text-II,D\text-IV}\) |
Subtopic: Relative Motion in One Dimension |
59%
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