Motion in a plane - Live Session Questions

The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as k = $a s^{2}$ where a is a constant. The force acting on the particle is
1.   $2 a \frac{s^{2}}{R}$
2.   $2 a s {(1 + \frac{s^{2}}{R^{2}})}^{1 / 2}$
3. 2as
4.   $2 a \frac{R^{2}}{s}$

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is
1. Zero
2. 30 $°$
3. 45 $°$
4. 60 $°$

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $a_{c}$ is varying with time t as, $a_{c}$ = $k^{2} r t^{2}$ , The power delivered to the particle by the forces acting on it is
1. $2 {πmk}^{2} r^{2} t$
2. ${mk}^{2} r^{2} t$
3. $\frac{m k^{4} r^{2} t^{5}}{3}$
4. Zero

The figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

1. 1, 2, 3, 4
2. 2, 3, 4, 1
3. 2, 4, 1, 2
4. 4, 3, 2, 1

The path of a projectile in the absence of air drag is shown in the figure by the dotted line. If the air resistance is not ignored then which one of the paths shown in the figure is appropriate for the projectile

1. B
2. A
3. D
4. C

The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are (0,2). The coordinates of another point at which the instantaneous velocity is same as the average point at which the instantaneous velocity is same as the average velocity between the points are

1. (1, 4)
2. (5, 3)
3. (3, 4)
4. (4, 1)

The light y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8 t - 5 t^{2})$ meter and x = 6t meter, where t is in second. The velocity with which the projectile is projected is
1. 8 m/sec
2. 6 m/sec
3. 10 m/sec
4. Not obtainable from the data

The range of a particle when launched at an angle of $15 °$ with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of $45 °$ to the horizontal
1. 1.5 km
2. 3.0 km
3. 6.0 km
4. 0.75 km

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is
1. 90 $°$
2. 60 $°$
3. 45 $°$
4. 30 $°$

10.

A stone projected with a velocity $u$ at an angle $θ$ with the horizontal reaches maximum height $H_{1}$ When it is projected with the velocity $u$ at an angle $(\frac{π}{2} - θ)$ with the horizontal, it reaches maximum height $H_{2}$ The relation between the horizontal range $R$ of the projectile, $H_{1}$ $$ and $H_{2}$ $$ is
1. $R = 4 \sqrt{H_{1} H_{2}}$
2. $R = 4 (H_{1} - H_{2})$
3. $R = 4 (H_{1} + H_{2})$
4. $R = \frac{{H_{1}}^{2}}{{H_{2}}^{2}}$

11.

For a given velocity, a projectile has the same range $R$ for two angles of projection if $t_{1}$ and $t_{2}$ are the times of flight in the two cases then
(1) $t_{1}$ $t_{2}$
(2) $t_{1}$ $t_{2}$
(3) $t_{1}$ $t_{2}$
(4) $t_{1}$ $t_{2}$

12.

A body of mass m is thrown upwards at an angle $\emptyset$ with the horizontal with velocity v. While up the velocity of the mass after t second will be
(1)   $\sqrt{{(v \cos \emptyset)}^{2} + {(v \sin \emptyset)}^{2}}$
(2) $\sqrt{{(v \cos \emptyset - v \sin \emptyset)}^{2} - g t}$
(3)   $\sqrt{v^{2} + g^{2} t^{2} - (2 v \sin \emptyset) g t}$
(4)   $\sqrt{v^{2}_g^{2} t^{2} - (2 v \cos \emptyset) g t}$

13.

A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about
1. 10 m
2. 7.5 m
3. 5 m
4. 2.5 m

14.

Four bodies P, Q, R and S are projected with equal velocities having angles of projection $15 °, 30 °, 45 ° and 60 °$ with the horizontal respectively. The body having shortest range is
1. P
2. Q
3. R
4. S

15.

A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is $(∠ P O Q = 40 °)$

1.   $2 v \cos 40 °$
2.   $2 v \sin 40 °$
3.   $2 v \sin 20 °$
4.   $2 v \cos 20 °$

16.

An aeroplane moving horizontally at a speed of 200 m/s and at a height of $8.0 \times 10^{3}$ m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released
1. 7.234 km
2. 8.081 km
3. 8.714 km
4. 9.124 km

17.

A cannon on a level plane is aimed at an angle $\emptyset$ above the horizontal and a shell is fired with a muzzle velocity vo towards a vertical cliff a distance D away. Then the height from the bottom at which the shell strikes the sidewalls of the chiff is
(1) $D \sin \emptyset - \frac{{g^{D}}^{2}}{2 {v_{0}}^{2} \sin^{2} \emptyset}$
(2) $D \cos \emptyset - \frac{g D^{2}}{2 {v^{2}}_{0} \cos^{2} \emptyset}$
(3) $D \tan \emptyset - \frac{g D^{2}}{2 u_{0}^{2} \cos^{2} \emptyset}$
(4) $D \tan \emptyset - \frac{g D 2}{2 {v_{0}}^{2} \sin^{2} \emptyset}$

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