Physics #letspractice (Motion in A Plane SET B - Easy)Contact Number: 8527521718Physics #letspractice (Motion in A Plane SET B - Easy)Contact Number: 8527521718Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:
1. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
A particle is moving such that its position coordinates \((x,y)\) are \( (2~\text m, 3~\text m)\) at time \(t=0,\) \( (6~\text m, 7~\text m)\) at time \(t=2~\text s\) and \( (13~\text m, 14~\text m)\) at time \(t=5~\text s.\) The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) is:
| 1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
| 3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero
A particle has an initial velocity \(\overrightarrow{u} = \left(4 \hat{i} - 5 \hat{j}\right)\) m/s and it is moving with an acceleration \(\overrightarrow{a} = \left(\frac{1}{4} \hat{i} + \frac{1}{5} \hat{j}\right)\text{m/s}^{2}\). Velocity of the particle at \(t=2\) s will be:
1. \((6\hat i -4\hat j)~\text{m/s}\)
2. \((4.5\hat i -4.5\hat j)~\text{m/s}\)
3. \((4.5\hat i -4.6\hat j)~\text{m/s}\)
4. \((6\hat i -4.6\hat j)~\text{m/s}\)
| 1. | \(5\) m | 2. | \(10\) m |
| 3. | \(20\) m | 4. | \(25\) m |
Two particles \(A\) and \(B\) are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:
| 1. | \( 1: 1 \) | 2. | \(r_A: r_B \) |
| 3. | \(v_A: v_B \) | 4. | \(r_B: r_A\) |
A person reaches a point directly opposite on the other bank of a flowing river while swimming at a speed of \(5~\text{m/s}\)at an angle of \(120^\circ\) with the flow. The speed of the flow must be:
1. \(2.5~\text{m/s}\)
2. \(3~\text{m/s}\)
3. \(4~\text{m/s}\)
4. \(1.5~\text{m/s}\)
For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)
A car is moving at a speed of \(40\) m/s on a circular track of radius \(400\) m. This speed is increasing at the rate of \(3\) m/s2. The acceleration of the car is:
1. \(4\) m/s2
2. \(7\) m/s2
3. \(5\) m/s2
4. \(3\) m/s2
An airplane is moving with a velocity \(u.\) It drops a packet from a height \(h.\) The time \(t\) taken by the packet to reach the ground will be:
1. \( \sqrt{\frac{2 g}{h}} \)
2. \( \sqrt{\frac{2 u}{g}} \)
3. \( \sqrt{\frac{h}{2 g}} \)
4. \( \sqrt{\frac{2 h}{g}}\)
