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1.

A block of mass \(m\) is being lowered by means of a string attached to it. The system moves down with a constant velocity. Then:
                                          

1.	the work done by gravity on the block is positive.
2.	the work done by force, \(F \) (the force of the string) on the block is negative.
3.	the work done by gravity is equal in magnitude to that done by the string.
4.	All of the above are true.

2.

A body constrained to move along the \({z}\)-axis of a coordinate system is subjected to constant force given by \(\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}\) where \(\hat{i},\hat{j} \) and \(\hat{k}\) are unit vectors along the \({x}\)-axis, \({y}\)-axis and \({z}\)-axis of the system respectively. The work done by this force in moving the body a distance of \(4~\text m\) along the \({z}\)-axis will be:
1. \(15~\text J\) 
2. \(14~\text J\) 
3. \(13~\text J\) 
4. \(12~\text J\) 

3.

A position dependent force \(F=7-2x+3x^2\) N acts on a small body of mass \(2\) kg and displaces it from \(x = 0\) to \(x = 5\) m. The work done in joule is:

1.	\(70\)	2.	\(270\)
3.	\(35\)	4.	\(135\)

4.

An object of mass \(m=1.5\) kg is acted upon by the force as shown in the figure that varies with the position of the object as shown. If the object starts from rest at a point \(x =0,\) then what is its speed at \(x = 50\) m?
                 
1. \(20\) m/s
2. \(25\) m/s
3. \(15\) m/s
4. \(17\) m/s

5.

The work done by a person in carrying a box of mass 10 kg to a vertical height of 10 m is 4900 J. The mass of the person is:
1.  40 kg
2.  60 kg
3.  50 kg
4.  55 kg

6.

A block of mass \(m\) initially at rest, is dropped from a height \(h\) onto a spring of force constant \(k.\) If the maximum compression in the spring is \(x,\) then:     
         
1. \(m g h = \frac{1}{2} k x^{2}\)
2. \(m g \left(h + x\right) = \frac{1}{2} k x^{2}\)
3. \(m g h = \frac{1}{2} k \left(x + h\right)^{2}\)
4. \(m g \left(h + x \right) = \frac{1}{2} k \left(x + h \right)^{2}\)${\mathrm{}}^{}$

7.

The potential energy of a particle varies with distance \(r\) as shown in the graph. The force acting on the particle is equal to zero at:

1. \(P\)
2. \(S\)
3. both \(Q\) and \(R\)
4. both \(P\) and \(S\)

8. A body initially at rest and sliding along a frictionless track from a height \(h\) (as shown in the figure) just completes a vertical circle of diameter \(AB=D \). The height \(h\) is equal to: 
              
1. \(\frac{3}{2}D\)
2. \(D\)
3. \(\frac{7}{4}D\)
4. \(\frac{5}{4}D\)

9. An automobile of mass \(m\) accelerates from rest, while the engine supplies constant power \(P.\) The speed of the automobile as a function of time, \(t\) is given by:
1. \(v=\left(\frac{2Pt}{m}\right)^{1/2}\)
2. \(v=\left(2Ptm\right)^{1/3}\)
3. \(v=\left(\frac{8Pt^3}{9m}\right)^{1/2}\)
4. \(v=\left(2Pt^3m\right)^{1/2}\)

10.

Which of the following remains unchanged (for the system) during an inelastic collision?

1.	Mechanical energy	2.	Kinetic energy
3.	Momentum	4.	All of the above.