Which one of the following satatement is true?

(a)

A scalar quantity is conserved in a process

(b)

A scalar quantity does not vary from one point to another in apace

(c)

A scalar quantity can never take -ve values

(d)

A scalar quantity has only magnitude and no direction.

The component of position vector \(\overrightarrow { r } \) along x-axis will maximum value if ____________

(a)

\(\overrightarrow { r } \) is along the x - axis

(b)

\(\overrightarrow { r } \) makes an angle of 45° with x - axis

(c)

\(\overrightarrow { r } \)  is along the y - axis

(d)

\(\overrightarrow { r } \)  is along - ve y - axis 

The length of a vector is _______________

(a)

always a negative quantity

(b)

always a positive quantity

(c)

either positive or negative

(d)

denoted by '\(\lambda \)' 

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

(a)

125 m

(b)

75 m

(c)

100 m

(d)

150 m

A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true?

(a)

Its speed is zero

(b)

Its acceleration is zero

(c)

Its acceleration is opposite to the velocity

(d)

Its speed may be variable

The velocity of a particle at an instant t is 10 m/s. After 5 s the velocity is 20 m/s. The velocity, 3 seconds earlier was ______________

(a)

2 m/s

(b)

3 m/s

(c)

4 m/s

(d)

5 m/s

s-t graph shown in figure is a parabola. From this graph we find that:

(a)

the body is moving with uniform velocity

(b)

the body is moving with uniform speed

(c)

the body is starting from rest and moving with uniform acceleration

(d)

the body is not moving at all

The acceleration of a moving body can be found from _____________

(a)

area under velocity-time graph

(b)

area under distance-time graph

(c)

slope of the velocity-time graph

(d)

slope of distance-time graph

The displacement of particle is given by X = a_o + \(\frac{a_1t}{2}-\frac{2_2t^2}{3}\) What is its acceleration?

(a)

\(\frac{2a_2}{3}\)

(b)

\(-\frac{2a_2}{3}\)

(c)

a₂

(d)

zero

The path of a particle moving under the influence of a force fixed in magnitude and direction is ______________

(a)

straight line

(b)

circle

(c)

parabola

(d)

ellipse

A man should hold his umbrella with vertical, when rain falls vertically with velocity \(\vec { { V }_{ R } } \) and man walks horizontally with velocity \(\vec{{V}_{M}}\) is _____________

(a)

\(tan^{-1}(\frac{\vec{V}_{M}}{\vec{V}_{R}})\)

(b)

\(tan^{-1}(\frac{\vec{V}_{R}}{\vec{V}_{M}})\)

(c)

tan^-1(V_R)

(d)

tan^-1(V_M)

Relative velocity of A with respect to B when A and B are in the opposite direction is ______________

(a)

\(\vec{V}_{A}-\vec{V}_{B}\)

(b)

\(\vec{V}_{B}-\vec{V}_{A}\)

(c)

\(\vec{V}_{A}+\vec{V}_{B}\)

(d)

\(\sqrt{V_A^2+2V_B^2+2V_AV_Bcos\theta}\)

Two stones of different masses are dropped simultaneously from the top of a building then ____________

(a)

smaller stone hit the ground earlier

(b)

larger stone hits the ground earlier

(c)

both stones reach the ground simultaneously

(d)

which of the stones reach the ground earlier depends on the composition of the stone

Two projectiles P and Q are fired from the same point with same velocity at angles 30° and 60°. The horizontal range of _____________

(a)

P is equal to Q

(b)

P is less than Q

(c)

P is greater than Q

(d)

none of the above

The maximum range of a gun of horizontal terrain is 16 km. If g = 10ms², then muzzle velocity of a shell must be _____________

(a)

160 ms^-1

(b)

200 \(\sqrt{2}\) ms^-1

(c)

400 ms^-1

(d)

800 ms^-1

Neglecting the air resistance, the time of flight of a projectile is determined by _____________

(a)

u_vertical

(b)

u_horizontal

(c)

u = u²_horizontal

(d)

u = u(u²_horizontal + u²_horizontal)^1/2

An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling ____________

(a)

on a parabolic path at seen by pilot in the plane

(b)

vertically along a straight path as seen by an observer on the ground near the target

(c)

on a parabolic path as seen by an observer on the ground near the target

(d)

on a zig-zag path as Seen by pilot in the plane'

The time of flight is __________ the time taken to attain the maximum height:

(a)

thrice

(b)

same

(c)

twice

(d)

four times

When a body undergoes an oblique projection, maximum range of it is ____________.

(a)

\(\frac{u^2}{g}\)

(b)

\(\frac{u}{g}\)

(c)

\(\frac{u^2}{g^2}\)

(d)

\(\frac{u^2}{2g}\)

The angle of projection for a projectile to cover maximum range is _______________

(a)

30°

(b)

60°

(c)

0°

(d)

45°

For a projectile, projected at an angle with the horizontal, the resultant velocity is _____________

(a)

\(\sqrt{u^2+g^2t^2-2utg\quad sin\theta}\)

(b)

\(\sqrt{u^2+g^2t^2}\)

(c)

\(\sqrt{u^2-g^2t^2}\)

(d)

\(\sqrt{u^2+g^2t^2+2utg\quad sin\theta}\)

Which of the following is true regarding projectile motion?

(a)

horizontal velocity of projectile is constant

(b)

vertical velocity of projectile is constant

(c)

acceleration is not constant

(d)

momentum is constant

A person performing a somersault is an example of__________motion.

(a)

circular

(b)

vibratory

(c)

linear

(d)

rotational

Electric charge is an example for_________quantity.

(a)

vector

(b)

fundamental

(c)

scalar

(d)

both (a) and (b)

What is the resultant vectors, when 2 vectors are at right angles to each other?

(a)

\(R=\sqrt{P^2+Q^2}\)

(b)

R = P + Q

(c)

R = P - Q

(d)

\(R=\sqrt \frac{P}{Q}\)

Two vectors act along the mutually perpendicular directions are called______vectors.

(a)

equal

(b)

opposite

(c)

orthogonal

(d)

orthogonal unit

\(\vec A\) and \(\vec B\) are perpendicular if \(\vec A\)· \(\vec B\) =  ______________

(a)

1

(b)

0

(c)

\(\infty \)

(d)

\(\frac {\vec A}{\vec B}\)

The parallelogram law of vector addition is equivalent to___________method.

(a)

polygon

(b)

coplanar

(c)

triangle

(d)

collinear

If for two vectors \(\bar A,\bar B\) \(\bar A\times\bar B=0\) then the vectors are ____________

(a)

perpendicular to each other

(b)

parallel to each other

(c)

act at an angle 60°

(d)

act at an angle 30°

Which of the following statements is/are not true?

(a)

v, a and s are vectors

(b)

Mass, energy, work are vectors

(c)

Vector has only magnitude whereas scalar has both magnitude and direction

(d)

both (b) and (c)

Two vectors \(\bar A\) and \(\bar B\) are such that \(\bar A \times\bar B=\bar C\) and A = B = C then angle between  \(\bar A\) and \(\bar B\) is: _______________

(a)

120°

(b)

90°

(c)

60°

(d)

30°

If \(\bar A\)and \(\bar B\) are two vectors which of the statement is wrong?

(a)

\(\bar A+\bar B=\bar B+\bar A\)

(b)

\(\bar A-\bar B=-(\bar B+\bar A)\)

(c)

\(\bar A\times\bar B=\bar B\times\bar A\)

(d)

\(\bar A.\bar B=\bar B.\bar A\)

For the figure, which of the following is correct?

(a)

\(\vec A+\vec B=\vec C\)

(b)

\(\vec B+\vec C=\vec A\)

(c)

\(\vec C+\vec A=\vec B\)

(d)

\(\vec A+\vec B+\vec C=0\)

It is found that \(\left|A+B\right|=\left|A\right|.\) This necessarily implies ____________.

(a)

B = 0

(b)

A, B are anti-parallel

(c)

A, B are perpendicular

(d)

\(A,B\le 0\)

The expression for time of flight of a projectile is t_f = _____________

(a)

\(\frac{\sin\theta}{g}\)

(b)

\(\frac{u\sin\theta}{g}\)

(c)

\(\frac{u\sin\theta}{2g}\)

(d)

\(\frac{2u\sin\theta}{2g}\)

The expression for horizontal range when a body is projected at an angle with the horizontal is R = ______________

(a)

\(\frac{u\sin\theta}{g}\)

(b)

\(\frac{u^2\sin\theta}{g}\)

(c)

\(\frac{u^2\sin\theta}{2g}\)

(d)

\(\frac{u^2\sin^2\theta}{2g}\)

The equation y = \(\frac{8}{2u^2}x^2\) represents ____________

(a)

the path of a freely falling body

(b)

the path of a thrown bodies

(c)

the path of a projectile

(d)

hyperbola

During a projectile motion if the maximum height equals the horizontal range, then the angle of projection with the horizontal is ______________.

(a)

tan^-1(1)

(b)

tan^-1(2)

(c)

tan^-1(3)

(d)

tan^-1(4)

The expression for maximum height attained when the body is projected at an angle with the horizontal is:

(a)

\(\frac{u\sin\theta}{2g}\)

(b)

\(\frac{u\sin^2\theta}{2g}\)

(c)

\(\frac{u^2\sin^2\theta}{g}\)

(d)

\(\frac{u^2\sin^2\theta}{2g}\)

If the length of the second hand in a stop clock is 3cm. The angular velocity and linear velocity of the tip is _______________

(a)

0.2047 rad/s; 0.0314 ms^-1

(b)

0.2547 rad/s; 0.314 ms^-1

(c)

0.1472 rad/s; 0.06314 ms^-1

(d)

0.1047 rad/s; 0.00314 ms^-1

When a body moves once circular path, the ______________

(a)

magnitude of velocity changes and its direction remain constant

(b)

magnitude of velocity remains constant and its direction changes continuously

(c)

magnitude of velocity remains constant and direction remains constant

(d)

magnitude of velocity and direction changes continuously

Dimension of angular velocity is ________________

(a)

MLT^-1

(b)

M⁰L⁰T^-1

(c)

MLT^-2

(d)

M⁰L⁰T^-2

Radial acceleration is _____________

(a)

\(v\omega^2\)

(b)

\(r\omega\)

(c)

\(r^2\omega\)

(d)

\(r\omega^2\)

A body moving with a constant speed v in a circle of radius r. Its angular acceleration is ______________

(a)

0

(b)

vr

(c)

\(\frac{v}{r}\)

(d)

\(\frac{v^2}{r}\)

If \(\omega_0,\omega\) are initial and final angular velocities, \(\theta\) is the angular displacement and a is the angular acceleration then _____________

(a)

\(\omega^2=\omega_0^2-2\alpha\theta\)

(b)

\(\omega_0^2=\omega^2-2\alpha\theta\)

(c)

\(\omega_0^2=\omega^2+2\alpha\theta\)

(d)

\(\omega^2=\omega_0^2+2\alpha\theta\)

A particle moving in a circular path of certain radius, with uniform angular velocity co has an angular acceleration equal to ______________

(a)

0

(b)

unity

(c)

infinity

(d)

insufficient data to calculate

In which direction of the motion of the particle does centripetal force act?

(a)

parallel

(b)

radial

(c)

tangential

(d)

right angle

A body is moving with a constant speed v in a circle of radius r. Its angular acceleration is _____________.

(a)

vr

(b)

\(\frac{v}{r}\)

(c)

zero

(d)

\(\frac{v}{r^2}\)

1 radian = ________.

(a)

50729°

(b)

572.9°

(c)

\(\frac{\pi}{180}\)

(d)

57.295°

The magnitude of the resultant of the 2 orthogonal vectors of 3 units and 4 unit is _____________.

(a)

7

(b)

25

(c)

5

(d)

1