Laws Of Motion-Test 01

Two particles A and B having mass m each and charge $$q_1$$ and $$-q_2$$ respectively, are connected at the ends of a non conducting flexible and inextensible string of the length l. The particle A is fixed and B is whirled along a vertical circle with centre at A. If a vertically upward electric field of strength E exists in the space, then for minimum velocity of particle B:

Rocket propulsion theory is analogues to-

Metal wire in the form of a ring of radius $$R$$ and mass m placed on a smooth horizontal table is set rotating about its own axis in such a way that each part of the ring moves with speed $$V$$.The tension in the ring Will be;-

In which example is it not possible for the underlined body to be in equilibrium?

The angle of banking $$\theta$$ for a cyclist taking curve is given by $$tan\theta=\dfrac { { v }^{ n } }{ rg }$$, where symbols( v= speed of the cyclist, r= radius of the curved path, g= acceleration due to gravity) have their usual meanings.Then the value of $$n$$ is equal to

A uniform bar of mass $$m$$ is supported by a pivot at its top about which the bar can swing like a pendulum. If a force $$F$$ is applied perpendicular to the lower end of the bar as shown in figure, what is the value of $$F$$ in order to hold the bar in equilibrium at an angle $$(\theta )$$ from the vertical

A heavy stone hanging from a massless string of length $$15$$m is projected horizontally with speed $$147$$ m/s. The speed of the particle at the point where the tension in the string equals the weight of the particle is?

A particle originally at rest at the hoghest point of a smooth vertical circle is slightly displaced. it will leave the circle at a vertical distance h below the highest point, such that h is equal to

A stone of mass $$0.3$$ kg attached to a $$1.5$$m long string is whirled around in a horizontal circle at a speed of $$6$$ m/s. The tension in the string is?

A block of mass 10 kg is suspended through two light spring balances as shown below