The dimensional formula for gravitational constant G is

(a)

[ML³T^-2]

(b)

[M^-1L³T^-2]

(c)

[M^-1L^-3T^-2]

(d)

[ML^-3T²]

The dimension of a quantity \(hy \over c\) where h is the planck's constants, \(\gamma\) is the frequency and c is the velocity of light are _______________.

(a)

MT^-1

(b)

MLT^-1

(c)

MLT^-2

(d)

ML²T²

Identify the pair of physical quantities having the same dimensions.

(a)

Light year and period of a pendulum

(b)

Angular momentum and torque

(c)

Energy and Modulus of elasticity

(d)

Torque and work

If E and B respectively, represent electric field and magnetic induction field, then the ratio \(\frac{E}{B}\) has the dimensions of _____________.

(a)

angle

(b)

acceleration

(c)

velocity

(d)

displacement

Which two of the following five physical parameters have the same dimensions?
1. energy density
2. refractive index
3. dielectric constant
4. Young's modulus
5. magnetic field

(a)

1 and 4

(b)

1 and 5

(c)

2 and 4

(d)

3 and 5

The time dependence of a Physical quantity p is given by P = P₀ exp(-at²) where a is a constant and t is the time. The constant a _____________.

(a)

is diemensionless

(b)

has dimensions[T^-2]

(c)

has dimensions[T²]

(d)

has dimensions of P

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

(a)

g = 20 ms^-2

(b)

g = 25 ms^-2

(c)

g = 15 ms^-2

(d)

g = 30 ms^-2

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 

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)

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)

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

If \(\bar A\) and \(\bar B\) denotes the sides of a parallelogram whose area is \(\frac{1}{1}\left| A \right|\left| B \right|\) the angle between \(\bar A\) and \(\bar B\) is _______________

(a)

60°

(b)

45°

(c)

30°

(d)

90°

What is the ratio of the angular speeds of the minute hand and second-hand of a clock?

(a)

1: 12

(b)

12: 1

(c)

1: 60

(d)

60: 1

A vector having unit magnitude is called________vector.

(a)

like

(b)

unlike

(c)

orthogonal

(d)

unit

Two masses m₁ and m₂ are experiencing the same force where m₁ < m₂.The ration of their acceleration \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \) is _____________.

(a)

1

(b)

less than 1

(c)

greater than 1

(d)

all the three cases

A body of mass 20 kg moving with a uniform velocity of 4 ms^-1. Then the net force acting on a body is _____________.

(a)

constant

(b)

increase

(c)

decrease

(d)

Zero

A body of mass M hits normally a rigid wall with velocity V and bounces back with the same velocity. The impulse experienced by the body is ______________.

(a)

MV

(b)

1.5 MV

(c)

2MV

(d)

zero

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

v

(b)

v²

(c)

v³

(d)

v⁴

A stationary particle explodes into two particles of masses m₁ and m₂, which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is ______________

(a)

m₂/m₁

(b)

m₁/m₂

(c)

1

(d)

m₁v₂/m₂v₁

The area covered under force and displacement graph is _______________.

(a)

work done

(b)

acceleration

(c)

power

(d)

kinetic energy

The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,

(a)

\( \sqrt \frac{4}{3}gh\)

(b)

\( \sqrt \frac{10}{7}gh\)

(c)

\(\sqrt{2gh}\)

(d)

\( \sqrt \frac{1}{2}gh\)

The mass of a body measures _______________.

(a)

density

(b)

centre of mass

(c)

moment of inertia

(d)

coefficient of inertia

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is _____________.

(a)

20ms^-1

(b)

30ms^-1

(c)

5ms^-1

(d)

10ms^-1

Two bodies of mass 1 kg and 3 kg have position vectors \(\hat { i } +2\hat { j } +\hat { k } \) and respectively. The centre of mass of this system has a position vector __________.

(a)

\(-2\hat { i } -\hat { j } +\hat { k } \).

(b)

\(2\hat { i } -\hat { j } -2\hat { k } \).

(c)

\(-\hat { i } +\hat { j } +\hat { k } \)

(d)

\(-2\hat { i } +2\hat { k } \).

Consider a system of two particles having masses m₁ and m₂ If the particle of mass m₁ is pushed towards the mass centre of particles through a distance d, by what distance would be particle of mass m₂ move so all to keep the mass centre of particles at the original position?

(a)

\(\frac { m_{ 1 } }{ { m }_{ 1 }+{ m }_{ 2 } } \)d

(b)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \)d

(c)

d

(d)

\(\frac { { m }_{ 2 } }{ { m }_{ 1 } } \)d

If the mass and radius of the Earth are both doubled, then the acceleration due to gravity g'

(a)

remains same

(b)

\({g\over 2}\)

(c)

2g

(d)

4g