Question 1 :
Two particles are moving along two long straight lines, in the same plane with same speed $\displaystyle 20\ cm/s.$ The angle between the two lines is $\displaystyle 60^{o}$ and their intersection point is $O$. At a certain moment, the two particles are located at distance $3\ m$ and $4\ m$ from $O$, and are moving towards $O$. Subsequently, the shortest distance between them will be<br>

Question 2 :
A particle P is fixed at certain point in horizontal plane and another particle Q is moving around P in circular path (with centre O) of radius 'r' with constant speed 'u'. 'P' observes the motion of 'Q'. Pick out<b> correct</b> statement :<br/><br/>

Question 3 :
A train is standing on a platform, a man inside a compartment of a train drops a stone. At the same instant train starts to move with constant acceleration. The path of the particle as seen by the person who drops the stone is:

Question 4 :
In projectile motion, the modulus of rate of change of speed.

Question 5 :
A trolley is moving horizontally with a velocity of v m/s w.r.t. earth. A man starts running in the direction of motion of trolley from one end of trolley with a velocity $1.5 v \ m/s$ w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running with a velocity of$ 1.5 v \ m/s$ w.r.t. trolley in the backward direction. If the length of the trolley is L, then the displacement of the man with respect to earth, measured as a function of time, will attain a maximum value of

Question 6 :
Ship A is located $4\ km$ north and $3\ km$ east of ship B. Ship A has a velocity of $20\ kmh^{-1}$ towards the south and ship B is moving at $40 \ kmh^{-1}$ in a direction $37^o$ north of east. X and Y axes are along east and north directions, respectively.

Question 7 :
When a man stands on a moving escalator he goes up in $40s$ and when he walked up the moving escalator he goes up in $20\ s$. The man walk up the stationary escalator in a time of:

Question 8 :
At the highest point of a projectile its velocity i half the initial velocity in magnitude The angle of projection from ground is

Question 9 :
Two particles $A$ and $B$ start simultaneously from the same point and move in a horizontal plane. $A$ has an initial velocity $u_{ 1 }$ due east and acceleration $a_{ 1 }$ due north. $B$ has an initial velocity $u_{ 2 }$ due north and acceleration $a_{ 2 }$ due east. Which of the following statements is(are) correct?<br>

Question 10 :
A large number of particles are moving towards each other with velocity $V$ having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs?<p></p>