MOTION IN A PLANE

The angle between A = iˆ + ˆj and B = ˆi - ˆj is

• 45 degrees

• - 45 degrees

• 90 degrees

• 180 degrees

Which one of the following statements is true?

• A scalar quantity is the one that is conserved in a process.

• A scalar quantity is the one that can never take negative values.

• A scalar quantity is the one that does not vary from one point

  to another in space.

• A scalar quantity has the same value for observers with

  different orientations of the axes.

Figure shows the orientation of two vectors u and v in the XY plane. If u=aiˆ +b ˆj and v = pˆi+ qˆj

which of the following is correct?

• a and p are positive while b and q are negative.

• a, p and b are positive while q is negative.

• a, q and b are positive while p is negative.

• a, b, p and q are all positive.

The component of a vector r, will have maximum along X-axis, if

• r is along positive Y-axis

• r is along positive X-axis

• r makes an angle of 45° with the X-axis

• r is along negative Y-axis

The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°, its range will be

• 60 m

• 71 m

• 100 m

• 141 m

Consider the quantities, pressure, power, energy, impulse,

gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are

• Impulse, pressure and area

• Impulse and area

• Area and gravitational potential

• Impulse and pressure

In a two dimensional motion, instantaneous speed v₀ is a positive constant. Then which of the following are necessarily true?

• The average velocity is not zero at any time.

• Average acceleration must always vanish.

• Displacements in equal time intervals are equal.

• Equal path lengths are traversed in equal intervals

It is found that |A+B|=|A|.This necessarily implies

• B = 0
  

• A,B are anti-parallel

• A,B are perpendicular

• $A.B\le0$

Two particles are projected in air with speed u at angles alpha and beta (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices

• angle of projection : alpha > beta

• time of flight : T₁ > T₂

• horizontal range : R₁ > R₂

• total energy : U₁ is greater than U₂

A particle slides down a friction less parabolic (y = x² ) track (A – B – C) starting from rest at point A (Fig). Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then

• KE at P = KE at B

• height at P = height at A

• total energy at P = total energy at A

• time of travel from A to B = time of travel from B to P.