A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30o, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

1. 0.6 and 0.6

2. 0.6 and 0.5

3. 0.5 and 0.6

4. 0.4 and 0.3

Subtopic:  Friction |
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A block A of mass ${\mathrm{m}}_{1}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass m2 is suspended. The coefficient of kinetic friction between block A and the table is ${\mathrm{\mu }}_{\mathrm{k}}$. When block A is sliding on the table, the tension in the string is:

1. $\frac{\left({\mathrm{m}}_{2}+{\mathrm{\mu }}_{\mathrm{k}}{\mathrm{m}}_{1}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$
2. $\frac{\left({\mathrm{m}}_{2}-{\mathrm{\mu }}_{\mathrm{k}}{\mathrm{m}}_{1}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$
3. $\frac{{\mathrm{m}}_{1}{\mathrm{m}}_{2}\left(1-{\mathrm{\mu }}_{\mathrm{k}}\right)\mathrm{g}}{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}$
4. $\frac{{\mathrm{m}}_{1}{\mathrm{m}}_{2}\left(1+{\mathrm{\mu }}_{\mathrm{k}}\right)}{{\mathrm{m}}_{1}+{\mathrm{m}}_{2}}\mathrm{g}$

Subtopic:  Friction |
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A system consists of three masses m1, m2, and m3 connected by a string passing over a pulley P. The mass m1 hangs freely, and m2 and m3 are on a rough horizontal table (the coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is : (Assume m1 = m2 = m3 = m)

1. $\frac{g\left(1-g\mu \right)}{9}$

2. $\frac{2g\mu }{3}$

3. $\frac{g\left(1-2\mu \right)}{3}$

4. $\frac{g\left(1-2\mu \right)}{2}$

Subtopic:  Friction |
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The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the  bottom if the coefficient of friction between the block and the lower half of the plane is given by:

1. μ = 2/tanθ
2. μ = 2tanθ
3. μ = tanθ
4. μ = 1/tanθ

Subtopic:  Friction |
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A car of mass m is moving on a level circular track of radius R. If ${\mu }_{s}$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by -

1. $\sqrt{Rg/{\mu }_{s}}$

2. $\sqrt{mRg/{\mu }_{s}}$

3. $\sqrt{{\mu }_{s}Rg}$

4.  $\sqrt{{\mu }_{s}mRg}$

Subtopic:  Friction |
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A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is µ = 0.5. The distance that the box will move relative to the belt before coming to rest on it, taking g = 10 ms–2 is:

1. 0.4 m

2. 1.2 m

3. 0.6 m

4. Zero

Subtopic:  Friction |
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A block of mass 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 |
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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 |
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A block B is pushed momentarily along a horizontal surface with an initial velocity 'v'. If μ is the coefficient of sliding friction between B and the surface, the block B will come to rest after a time:

1. $\frac{v}{g\mu }$

2. $\frac{g\mu }{v}$

3. $\frac{g}{v}$

4. $\frac{v}{g}$

Subtopic:  Friction |
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