Two bodies of equal masses are projected, one from top of the tower in the horizontal direction and other from the foot of tower at an angle of 45° with the horizontal, then the acceleration of their center of mass is
(1) downward
(2) g downward
(3) downward
(4) upward
A projectile is projected at an angle of 60° from horizontal. At an instant, it is moving at an angle of 30° with horizontal with velocity 10 m/s. The radial acceleration of the particle at that instant is:
1.
2.
3.
4.
The initial velocity of a projectile is given by m/s. If acceleration due to gravity is g = 10() m/, then the time after which projectile returns to the same horizontal level is:
(1) 4 s
(2) 10 s
(3) 14 s
(4) 12 s
Two persons start moving along two crossroads with the same speed 5 m/s. One in the direction of north and other is in the direction of the east as shown in the figure. Angular velocity of A with respect to B is :
(1) 0.5 m/s
(2) Zero
(3) 1.0 m/s
(4) 2 m/s
In projectile motion, accelerations of the projectile when it is gaining height and losing height respectively are
(1) g upward, g upward
(2) g upward, g downward
(3) g downward, g downward
(4) g downward, g upward
A person, who can swim with speed \(u\) relative to water, wants to cross a river (of width \(d\) and water is flowing with speed \(v\)). The minimum time in which the person can do so is:
1. \(\frac{d}{v}\)
2. \(\frac{d}{u}\)
3. \(\frac{d}{\sqrt{v^{2} + u^{2}}}\)
4. \(\frac{d}{\sqrt{v^{2} - u^{2}}}\)
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
Velocity and acceleration vectors of a particle moving on a circular path are shown here. At the instant shown:
(1) The speed of the particle must be decreasing.
(2) Acceleration of particle must be increasing in magnitude.
(3) The dot product of and is positive.
(4) The magnitude of the momentum of the particle must be increasing in magnitude.
A cricketer can throw a ball to a maximum horizontal distance of 50 m. How much high above the ground can he throw the same ball?
(1) 50 m
(2) 25 m
(3) 75 m
(4) 100 m