A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?
1. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the tangent to the circle. |
2. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius towards the centre. |
3. | \(\frac{\pi^2}{4} \mathrm{~ms}^{-2}\) and direction along the radius towards the centre. |
4. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius away from the centre. |
Two particles are projected with the same initial velocity, one makes an angle θ with the horizontal while the other makes an angle θ with the vertical. If their common range is R, then the product of their time of flight is directly proportional to:
1. R
2.
3.
4.
A particle (A) is dropped from a height and another particle (B) is projected in a horizontal direction with a speed of 5 m/s from the same height. The correct statement, from the following, is:
1. | Particle (A) will reach the ground first with respect to particle (B) |
2. | Particle (B) will reach the ground first with respect to particle (A) |
3. | Both particles will reach the ground at the same time |
4. | Both particles will reach the ground at the same speed |
A particle moves along a circle of radius \({{20}\over{\pi}} m\) with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is:
1. 40 ms–2
2. 640π ms–2
3. 160π ms–2
4. 40π ms–2
The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:
1. | \(4\) m/s \(53^\circ\) with x-axis |
2. | \(4\) m/s \(37^\circ\) with x-axis |
3. | \(5\) m/s \(53^\circ\) with y-axis |
4. | \(5\) m/s \(53^\circ\) with x-axis |
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0ĵ ) . What is the y-coordinate of the particle at the instant its x-coordinate is 84 m?
1. 36 m
2. 26 m
3. 1 m
4. 0 m
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) . What is the speed of the particle at the instant its x-coordinate is 84 m?
1. | 36 m/s | 2. | 26 m/s |
3. | 1 m/s | 4. | 0 m/s |
If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) & \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?
1. | time of flight |
2. | horizontal range of projectile |
3. | maximum height acquired |
4. | all of the above |
A particle moves in the \((x\text-y)\) plane according to the rule \(x = a sin (\omega t)\) and \(y = a cos (\omega t)\). The particle follows:
1. | a circular path. |
2. | a parabolic path. |
3. | a straight line path inclined equally to x and y-axes. |
4. | an elliptical path. |
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
1. 15º
2. 30º
3. 45º
4. 60º