1
AIPMT 2015
+4
-1
If vectors $$\overrightarrow A = \cos \omega t\widehat i + \sin \omega t\widehat j$$ and $$\overrightarrow B = \cos {{\omega t} \over 2}\widehat i + \sin {{\omega t} \over 2}\widehat j$$ are functions of time, then the value of t at which they are orthogonal to each other is
A
$$t = {\pi \over \omega }$$
B
t $$=$$ 0
C
$$t = {\pi \over {4\omega }}$$
D
$$t = {\pi \over {2\omega }}$$
2
AIPMT 2015
+4
-1
The positions vector of a particle $$\overrightarrow R$$ as a function of time is given by $$\overrightarrow R$$ = 4sin(2$$\pi$$t)$$\widehat i$$ + 4cos(2$$\pi$$t)$$\widehat j$$. Where R is in meters, t is in seconds and $$\widehat i$$ and $$\widehat j$$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
A
Magnitude of the velocity of particle is 8 meter/second.
B
Path of the particle is a circle of radius 4 meter.
C
Acceleration vector is along $$-$$$$\overrightarrow R$$.
D
Magnitude of acceleration vector is $${{{v^2}} \over R}$$
where v is the velocity of particle.
3
AIPMT 2015 Cancelled Paper
+4
-1
A ship A is moving Westwards with a speed of 10 km h$$-$$1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h$$-$$1. The time after which the distance between them becomes shortest, is
A
$$5\sqrt 2$$ h
B
$$10\sqrt 2$$ h
C
0 h
D
5 h
4
AIPMT 2014
+4
-1
A projectile is fired from the surface of the earth with a velocity of 5 m s$$-$$1 and angle $$\theta$$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m s$$-$$1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s$$-$$2) is
(Given g = 9.8 m s$$-$$2)
A
3.5
B
5.9
C
16.3
D
110.8
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