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1. If \(F=\alpha t^2-\beta t \) is the magnitude of the force acting on a particle at an instant \(t,\) then the time at which the force becomes constant is (where \(\alpha \) and \(\beta \) are constants):

1.	\(\dfrac{\beta}{\alpha}\)	2.	\(\dfrac{\beta}{2\alpha}\)
3.	\(\dfrac{2\beta}{\alpha}\)	4.	zero

2. A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
   $\mathrm{}$

1.	\(\overrightarrow N+\overrightarrow T+\overrightarrow W=0\)	2.	\(T^2=N^2+W^2\)
3.	\(T = N + W\)	4.	\(N = W \tan \theta\)

3. Given below are two statements:

Assertion (A):	A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back.
Reason (R):	In the absence of friction, the floor of the bus would slip forward under the feet of the passenger.

 

1.	(A) is True but (R) is False.
2.	(A) is False but (R) is True.
3.	Both (A) and (R) are True and (R) is the correct explanation of (A).
4.	Both (A) and (R) are True but (R) is not the correct explanation of (A).

4. A person holding a rifle (mass of person and rifle together is \(100\) kg) stands on a smooth surface and fires \(10\) shots horizontally, in \(5\) s. Each bullet has a mass of \(10~\mathrm{g}\) with a muzzle velocity of \(800\) ms^-1. The final velocity acquired by the person and the average force exerted on the person are: 
1. \(-0.08~ \text{ms}^{-1} ; 16~ \text{N} \)
2. \(-0.8~ \text{ms}^{-1} ; 16~ \text{N} \)
3. \(-1.6~ \text{ms}^{-1} ; 16~ \text{N} \)
4. \(-1.6 ~\text{ms}^{-1} ; 8 ~\text{N}\)

5.

A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is \(10\) ms^-1 and its base makes an angle \(\alpha=60^\circ\) with horizontal, then the vertical velocity of its end \(\mathrm{B}\) (in ms^-1) will be:
               

1.	\(10\sqrt{3}\)	2.	\(\frac{10}{\sqrt{3}}\)
3.	\(5\sqrt{3}\)	4.	\(\frac{5}{\sqrt{3}}\)

6.

If \(\mu\) between block \(A\) and inclined plane is \(0.5\) and that between block \(B\) and the inclined plane is \(0.8,\) then the normal reaction between blocks \(A\) and \(B\) will be:
                       
1. \(180~\text N\) 
2. \(216~\text N\) 
3. \(0\)
4. none of these

7.

The reading of spring balance in the depicted figure will be:
         

1.	\(0\) N	2.	\(20\) N
3.	\(10\) N	4.	\(5\) N

8.

A tube of length \( L\) is filled completely with an incompressible liquid of mass \(M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega\). The force exerted by the liquid at the other end is:

1.	\(ML \omega^2 \over 2\)	2.	\(ML^2 \omega \over 2\)
3.	\(ML \omega^2 \)	4.	\(ML^2 \omega^2 \over 2\)

9. A car is moving on a circular track of radius \(50~\text{cm}\) with coefficient of friction being \(0.34.\) On this horizontal track, the maximum safe speed for turning is equal to:
(take \(g=10~\text{m/s}^2\) )
1. \(1.03~\text{m/s}\)
2. \(1.7~\text{m/s}\) 
3. \(1.3~\text{m/s}\)
4. \(1.8~\text{m/s}\) 

10. Given below are two statements: 

Assertion (A):	Centripetal forces and centrifugal forces never cancel out.
Reason (R):	They do not act at the same time.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	(A) is False but (R) is True.