$A$ particle of mass $m$ is executing uniform circular motion on a path of radius $r$. If $p$ is the magnitude of its linear momentum,then the radial force acting on the particle is:

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$(a)$ For vectors $\vec{A} = 3\hat{i} + 2\hat{j}$ and $\vec{B} = \hat{i} + \hat{j} - 2\hat{k}$,the $y$-component of the vector $(\vec{A} - \vec{B})$ is .....
$(b)$ The formula for the total time of flight of a projectile projected vertically upwards with an initial velocity $u$ is ..........
$(c)$ The formula for the centripetal acceleration of a particle moving in a circular path of radius $R$ with a constant angular velocity $\omega$ is ......
$(d)$ The component of any vector is always .........

$A$ body of mass $1\, kg$ tied to one end of a string is revolved in a horizontal circle of radius $0.1\, m$ with a speed of $3$ revolutions per second. Assuming the effect of gravity is negligible,the linear velocity,acceleration,and tension in the string will be:

$A$ projectile of mass $m$ is fired with velocity $v$ from the point $P$ at an angle $45^{\circ}$ with the horizontal. The magnitude of change in momentum,when it passes through the point $Q$ on the same horizontal line on which $P$ lies,is :

$A$ charged particle of mass $m = 2 \ kg$ and charge $q = 1 \ \mu C$ is projected from a horizontal ground at an angle $\theta = 45^{\circ}$ with speed $u = 10 \ ms^{-1}$. In space,a horizontal electric field $E = 2 \times 10^7 \ NC^{-1}$ exists in the direction of projection. The range of the projectile is......$m$.

$A$ projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is