A particle is moving along a circular path with a constant speed of \(10\,ms^{-1}.\) What is the magnitude of the change in velocity of the particle, when it moves through an angle of \(60^{o}\) around the centre of the circle .......... \(m/s\)

A particle is executing simple harmonic motion \((SHM)\) of amplitude \(A,\) along the \(x-\) axis, about \(x = 0.\) When its potential energy \((PE)\) equals kinetic energy \((KE),\) the position of the particle will be

Given below in the left column are different modes of communication using the kinds of waves given in the right column

\(A.\) Optical Fiber Communication	\(P.\) Ultrasound
\(B.\) Radar	\(Q.\) Infrared Light
\(C.\) Sonar	\(R.\) Microwaves
\(D.\) Mobile Phones	\(S.\) Radio Waves

From the options given below, find the most appropriate match between entries in the left and the right column

The vertical component of the earth's magnetic field is \(6 \times 10^{-5} T\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\) Given \(\left.\tan 37^{\circ}=\frac{3}{4}\right)\)

A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

A man grows into a giant such that his linear dimensions increase by a factor of \(9\). Assuming that his density remains same, the stress in the leg will change by a factor of

A \(d.c.\) main supply of \(e.m.f.\, 220\, V\) is connected across a storage battery of \(e.m.f.\, 200\, V\) through a resistance of \(1\,\Omega \). The battery terminals are connected to an external resistance \('R'\) . The minimum value of \('R'\), so that a current passes through the battery to charge it is ............... \(\Omega\)

The current \((i)\) at time \(t =0\) and \(t =\infty\) respectively for the given circuit is

A rectangular block of mass \(5\,kg\) attached to a horizontal spiral spring executes simple harmonic motion of amplitude \(1\,m\) and time period \(3.14\,s\). The maximum force exerted by spring on block is \(.......N\).

Given below are two statements : Statement \(I\) : In an \(LCR\) series circuit, current is maximum at resonance. Statement \(II\) : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below :

The displacement time graph of a particle executing \(S.H.M.\) is given in figure: (sketch is schematic and not to scale) Which of the following statements is are true for this motion? \((A)\) The force is zero \(t=\frac{3 T}{4}\) \((B)\) The acceleration is maximum at \(t=T\) \((C)\) The speed is maximum at \(t =\frac{ T }{4}\) \((D)\) The \(P.E.\) is equal to \(K.E.\) of the oscillation at \(t=\frac{T}{2}\)