# A block of mass $$\mathrm{m}$$ is in contact with the cart C as shown in the figure.           The coefficient of static friction between the block and the cart is $\mathrm{\mu }$. The acceleration $\mathrm{\alpha }$ of the cart that will prevent the block from falling satisfies: 1. $\mathrm{\alpha }>\frac{\mathrm{mg}}{\mathrm{\mu }}$ 2. $\mathrm{\alpha }>\frac{\mathrm{g}}{\mathrm{\mu m}}$ 3. $\mathrm{\alpha }\ge \frac{\mathrm{g}}{\mathrm{\mu }}$ 4. $\mathrm{\alpha }<\frac{\mathrm{g}}{\mathrm{\mu }}$

Subtopic:  Friction |
82%
From NCERT
AIPMT - 2010
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A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if:

1. $r=\mu g{\omega }^{2}$

2. $r<\frac{{\omega }^{2}}{\mu g}$

3. $r\le \frac{\mu g}{{\omega }^{2}}$

4. $r\ge \frac{\mu g}{{\omega }^{2}}$

Subtopic:  Friction |
67%
From NCERT
AIPMT - 2010
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An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, the first part 1 kg moving with a velocity of 12 ${\mathrm{ms}}^{-1}$ and the second part 2 kg moving with a velocity of 8 ${\mathrm{ms}}^{-1}$. If the third part flies off with a velocity of 4 ${\mathrm{ms}}^{-1}$, its mass would be:

1. 5 kg
2. 7 kg
3. 17 kg
4. 3 kg

Subtopic:  Newton's Laws |
77%
From NCERT
AIPMT - 2009
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The mass of a lift is $$2000$$ kg. When the tension in the supporting cable is $$28000$$ N, then its acceleration is:
(Take $$g=10$$ m/s2)

 1 $$30$$ ms-2 downwards 2 $$4$$ ms-2 upwards 3 $$4$$ ms-2 downwards 4 $$14$$ ms-2 upwards
Subtopic:  Application of Laws |
84%
From NCERT
AIPMT - 2009
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A body, under the action of a force $$\overset{\rightarrow}{F} = 6 \hat{i} - 8 \hat{j} + 10 \hat{k}$$, acquires an acceleration of 1 ms-2. The mass of this body must be:

1. 2 √10 kg

2. 10 kg

3. 20 kg

4. 10 √2 kg

Subtopic:  Newton's Laws |
87%
From NCERT
AIPMT - 2009
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A roller coaster is designed such that riders experience "weightlessness" as they go around the top of a hill whose radius of curvature is $$20$$ m. The speed of the car at the top of the hill is between:
 1 $$14$$ m/s and $$15$$ m/s 2 $$15$$ m/s and $$16$$ m/s 3 $$16$$ m/s and $$17$$ m/s 4 $$13$$ m/s and $$14$$ m/s
Subtopic:  Uniform Circular Motion |
71%
From NCERT
AIPMT - 2008
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Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:
1.  Mv Newton

2.  2Mv Newton

3.  $\frac{\mathrm{Mv}}{2}$ Newton

4.  zero

Subtopic:  Newton's Laws |
67%
From NCERT
AIPMT - 2008
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A block $$B$$ is pushed momentarily along a horizontal surface with an initial velocity $$v.$$ If $$\mu$$ is the coefficient of sliding friction between $$B$$ and the surface, the block $$B$$ will come to rest after a time:

1. $$v \over g \mu$$
2. $$g \mu \over v$$
3. $$g \over v$$
4. $$v \over g$$

Subtopic:  Friction |
79%
From NCERT
AIPMT - 2007
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A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of ${30°}^{\mathrm{}}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is:

1. 48 N

2. 24 N

3. 12 N

4. 96 N

Subtopic:  Application of Laws |
76%
From NCERT
AIPMT - 2006
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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 $$ML^2 \omega^2 \over 2$$
Subtopic:  Uniform Circular Motion |
57%
From NCERT
AIPMT - 2006
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