Force and Laws of Motion

A block of mass

[

*m*_{1}=1 kg another mass*m*_{2}= 2 kg, are placed together (see figure) on an inclined plane with angle of inclination*θ*. Various values of*θ*are given in List I. The coefficient of friction between the block*m*_{1}and the plane is always zero. The coefficient of static and dynamic friction between the block*m*_{2}and the place are equal to*μ*= 0.3. In List II, expressions for the friction on block*m*_{2}_{ }are given. Match the correct expression of the friction in List II with the angles given in List I and choose the correct option. The acceleration due to gravity is denoted by*g*.[

**Useful information:**tan (5.5°) ≈ 0.1; tan (11.5°) ≈ 0.2; tan (16.5°) ≈ 0.3]List I |
List II |
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P. |
θ = 5° |
1. |
m_{2}gsin θ |

Q. |
θ = 10° |
2. |
(m_{1} + m_{2})gsin θ |

R. |
θ = 15° |
3. |
μm_{2}gcos θ |

S. |
θ = 20° |
4. |
μ(m_{1} + m_{2})gcos θ |

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JEE Advanced 2014

In the following figure two spheres are connected by a light spring of spring constant

*k*. The system of the two spheres is placed inside a liquid container of density 2ρ.

The information for the two spheres is as follows:-

Radius | Density | |

upper sphere | R |
ρ |

downer sphere | R |
3ρ |

If at a certain instant of time the system of spheres and spring is in equilibrium then

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JEE Advanced 0