Laws of Motion

Sand is being dropped from a stationary dropper at a rate of 0.5 kgs^-1 on a conveyor belt moving with a velocity of 5ms^-1. The power needed to keep the belt moving with the same velocity will be:

A block of mass 200g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F $=\sqrt[]{x}$ N as shown in figure.

A curved in a level road has  aradius 75m. The maximum speed of a car turning this curved road can be 30 m/s without skidding.; If radius of curved road is changed to 48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be…….m/s.

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega .$ <!-- [if gte mso 9]><xml> </xml><![endif]--> The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$ <!-- [if gte mso 9]><xml> </xml><![endif]-->. The beaker will revolve with the disc if :

A system of two blocks of masses m = 2kg and M = 8kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocked is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be:

A mass of $10\mathrm{k}\mathrm{g}$ is suspended by a rope of length $4\mathrm{m}$ , from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of ${45}^{?}$ with the vertical. Then $\mathrm{F}$ equals: (Take $\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}$  and the rope to be massless)
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Two bodies of masses m₁ = 5kg and m₂ = 3kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m₁ will be:

 [Take g = 10 ms^-2]

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> the spring constant is _________ Nm^-1. (Use g = 10 ms^-2)

A block of mass 10 kg, starts sliding on a surface with an initial velocity of 9.8 ms^-1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is :                                                                                                            

[used g = 9.8 ms^-2]

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1cm on main scale and 50 Vernier scale divisions are equal to 49 main scale division, then least count of the travelling microscope is __________× 10^-6 m.