Laws of Motion

Statement I: A cyclist is moving on an un-banked road with a speed of 7 kmh?¹ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2 The cyclist will not slip and pass the curve. (g = 9.8m/s²)
Statement II: If the road is at an angle of 45°, cyclist can cross of the curve of 2m radius with the speed of 18.5 kmh?¹ without slipping
In the light of the above statements, choose the correct the answer from the options given below.

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be:

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega rpm$ . The tension in the string is $T$ . If speed becomes $2\omega$  while keeping the same radius, the tension in the string becomes:

A $10\mu F$ capacitor is connected to a $210 V,50 Hz$ source as shown in figure. The peak current in the circuit is nearly ( $\pi =3.14$  ):

The output $\left(Y\right)$  of the given logic gate is similar to the output of an/a

When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and though the same distance, it takes time aT, where a is a constant greater than 1. The co-efficient of friction between the body and the rough plane is   $\frac{1}{\sqrt[]{x}}\left(\frac{{\alpha }^2-1}{\alpha }\right)$ where x =___________.

A horizontal force 10 N is applied to a block $A$ as shown in figure. The mass of blocks $A$ and $B$ are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block $A$ on block $B$  is :

Two bodies $A$ and $B$ of same mass undergo completely inelastic one dimensional collision. The body $A$ moves with velocity $v_1$ while body $B$ is at rest before collision. The velocity of the system after collision is $v_2$ . The ratio $v_1:v_2$  is

A sheet block of 10kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s². The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20kg each, is_________N.

[Take g = 10 m/s² and ${\mu }_s=0.2]$  

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt[]{x}}{5}$  if the time of ascent is half of the time of descent. The value of x is__________.