A bullet is fired with a speed of $1000m/\sec$ in order to hit a target 100 m away. If $g=10m/s^2$, the gun should be aimed:

(1) Directly towards the target

(2) 5 cm above the target

(3) 10 cm above the target

(4) 15 cm above the target

A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top? 

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is $30°$) is:

A ball is dropped from the top of a tower of 100m height. Simultaneously another ball is thrown upwards from the bottom of the tower with a speed of 50 m/s ($g=10m/s^2$). They will cross each other after:

1. 1 s

2. 2 s

3. 3 s

4. 4 s

Read the assertion and reason carefully to mark the correct option out of the options given below:

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

(5) If assertion is false but reason is true.

Assertion : Rocket in flight is not an illustration of projectile.

Reason : Rocket takes flight due to combustion of fuel and does not move under the gravity effect alone.

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:

1. v²/r

2. vr

3. v/r

4. r/v

Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:
1. \(m_1:m_2\)
2. \(r_1:r_2\)
3. \(1:1\)
4. \(m_1r_1:m_2r_2\)

If a particle moves in a circle describing equal angles in equal times, its velocity vector:

(1) remains constant.

(2) changes in magnitude.

(3) changes in direction.

(4) changes both in magnitude and direction.

A motorcyclist going round in a circular track at a constant speed has:

(1) constant linear velocity.

(2) constant acceleration.

(3) constant angular velocity.

(4) constant force.

A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio 

(1) 1 : 1

(2) 1 : 2

(3) 2 : 1

(4) 4 : 1