The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

How many \(\mu\)m present in one metre?

The speed of an object v = 40 ms^-1. The same quantity of speed in kmh^-1 is _____________.

SI unit of the universal constant of gravitation (G) is ______________.

While measuring acceleration due to gravity, by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error , of 3% in the value of time period. The percentage error in the measurement of 'g' is _______________.

If a particle has negative velocity and negative acceleration, its speed

If one object is dropped vertically downward and another object is thrown horizontally from the same height, then the ratio of vertical distance covered by both objects at any instant t is

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

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

Choose the motion in two dimension from the following.

A book is at rest on the table which exerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton's third law?

When the object is moving at constant velocity on the rough surface

The centrifugal force appears to exist

A body of mass 30 kg climbs on a rope. The boy climbs up with an acceleration of 5 ms^-2 What is the tension of a rope?

No force is required for ____________.

Using a screw gauge the thickness of a wire was measured as Smm. Calculate
(i) the fractional error
(ii) the percentage error
Given data:
Thickness of the wire (t) = 5mm
Accuracy \(\triangle t\)= 0.01mm

When the planet Jupiter is at a distance of 824.7 million kilometers from the earth. its angular diameter is measured to be 35.72 of arc. Calculate the diameter of Jupiter.

In a submarine fitted with a SONAR, the time delay between generation of a signal and reception of its echo from an enemy ship is 110.3 seconds. If speed of sound in water is 1450 ms^-1  then calculate the distance of the enemy ship from the submarine.

What is meant by frame of reference?

Distinguish between distance and displacement.

Explain the concept of a function.

Define relative velocity.

A gun is fired from a place which is at distance 1.2 km from a hill. The echo of the sound is heard back at the same place of firing after 8 second. Find the speed of sound.

Give examples for inertia frames

Write second law of motion in the derivative of position vector form.

What are the forces acting on the sliding object?

What are the forces acting on the vehicle when it moves in circulated road?

Consider a circular leveled road of radius 10m having coefficient of static friction 0.81. Three cars (A, B and C) are travelling with speed 7 ms^-1, 8 m s^-1 and 10 ms^-1 respectively. Which car will skid when it moves in the circular level road? (g = 10 m s^-2).

Briefly explain the types of physical quantities.

How will you measure the diameter of the Moon using parallax method?

Show that a screw gauge of pitch 1mm and 100 divisions is more precise than a vernier caliper with 20 divisions on the sliding scale.

In a physical units, how many units are there in 1 metre?
1 parallactic second (parsec) = 3.08\(\times\)10¹⁶ m
Given data:
1 AU = 1.496\(\times\)10¹¹m
1 ly = 9.467\(\times\)10¹⁵m
1 mm = 10^-6m
1 parsec = 3.08\(\times\)10¹⁶m

The Moon subtends an angle of 1⁰ 55' at the base line equal to the diameter of the earth. What is the distance of the Moon from the Earth? (Radius of the Earth is 6.4\(\times\)10⁶m)

What does the slope of 'position-time' graph represent? Which physical quantity is obtained from it?

Write an expression for the two objects, moving with uniform velocities along the same straight tracks but opposite in direction.

How can the depth of well is measured and also estimate the % of real error.

The velocity of three particles A, B, C are given below. Which particle travels at the greatest speed?
\(\vec {v_A}=3\hat i+5\hat j+2\hat k\)
\(\vec {V_B}=\hat i+2\hat j+3\hat k\)
\(\vec{V_C}=5\hat i+3\hat j+4\hat k\)

In the cricket game, a batsman strikes the ball such that it moves with the speed 30 ms^-1 at an angle 30° with the horizontal as shown in the figure. The boundary line of the cricket ground is located at a distance of 75 m from the batsman? Will the ball go for a six? (Neglect the air resistance and take acceleration due to gravity g = 10 m s^-2).

Briefly explain on Aristotle vs. Newton's approach on sliding object.

A boy throws ball of mass 100 g with a speed of 15 m/s, If the ball hits a wall and rebounds with the half the original speed, what is the change in momentum of the ball?

A bomb of mass 30 kg, initially at rest explodes into three pieces of masses. m₁ = m₂ = 20 kg. If the kinetic energy of two pieces (m₁ = m₂) is 400 J. Calculate the kinetic energy of the third piece.

A 40 gm of bullet moving at 250 ms^-1 stops after penetrating 20 cm of wood. Calculate the average force exerted by the bullet.

Calculate the centripetal acceleration of the Earth which orbits around the Sun. The Sun to Earth distance is approximately 150 million km. (Assume the orbit of Earth to be circular).

In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 sec. If the speed of sound in water is 1460 ms^-1. What is the distance of enemy submarine?

The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.

If the value of universal gravitational constant in SI is 6.610^-11Nm^-2kg^-2, then find its value in CGS System?

The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k = 1)

Convert 76 cm of mercury pressure into Nm^-2 using the method of dimensions.

Convert the vector \(\vec { r } =3\hat { i } +2\hat { j } \) into a unit vector.

What are the resultants of the vector product of two given vectors given by \(\overrightarrow { A } =4\hat { i } -2\hat { j } +\hat { k } \ and \ \overrightarrow { B } =5\hat { i } +3\hat { j } -4\hat { k } \)

An object at an angle such that the horizontal range is 4 times of the maximum height. What is the angle of projection of the object?

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is
(a) 30° 
(b) 45° 
(c) 150°
(d) 120°

Explain triangular law of addition method.

Calculate the centripetal acceleration of Moon towards the Earth.

Find
(i) acceleration
(ii) speed of the sliding object using free body diagram.

A spider of mass 50 g is hanging on a string of a cob web. What is the tension in the string?

A bob attached to the string oscillates back and forth. Resolve the forces acting on the bob into components. What is the acceleration experience by the bob at an angle ፀ.

A block of mass m slides down the plane inclined at an angle 60° with an acceleration \(\frac { g }{ 2 } \). Find the coefficient of kinetic friction.