Three different objects of mass $m_1,$ $m_2$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:

1.	$m_1:m_2:m_3$	2.	$m_1:2m_2:3m_3$
3.	1 : 1 : 1	4.	$\frac{1}{m_1}:\frac{1}{m_2}:\frac{1}{m_3}$

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle 

1. $\frac{m{v}^2}{r}\times \pi r$

2. Zero

3. $\frac{m{v}^2}{r^2}$

4. $\frac{\pi r^2}{m{v}^2}$

A ball is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension:

1. gl

2. 2 gl

3. $\sqrt{gl}$

4. $\sqrt{2gl}$

A body of mass m hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of 60° with the vertical. The tension in the string at mean position is 

1. 2 mg

2. mg

3. 3 mg

4. $\sqrt{3}mg$

Which of the following graph depicts spring constant k versus length l of the spring correctly

1.
2.
3.
4.

Work done by a frictional force is

1. Negative

2. Positive

3. Zero

4. All of the above

A block of mass 50 kg slides over a horizontal distance of 1 m. If the coefficient of friction between their surfaces is 0.2, then work done against friction is 

1. 98 J

2. 72J

3. 56 J

4. 34 J

A man pushes a wall and fails to displace it. He does:
1. negative work
2. positive but not maximum work
3. no work at all
4. maximum work

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is

(1) 0°

(2) 30°

(3) 60°

(4) 90°

A force $F=(5\hat{i}+3\hat{j})$ newton is applied over a particle which displaces it from its origin to the point $r=(2\hat{i}-1\hat{j})$  metres. The work done on the particle is 

(1) – 7 joules

(2) + 13 joules

(3) + 7 joules

(4) + 11 joules