$A$ car moving with a linear speed of $72 \ km/h$ has wheels of radius $0.250 \ m$. If the wheels come to rest after $20$ rotations upon applying brakes,the angular retardation produced by the brakes is ....... $rad \ s^{-2}$. (in $.5$)

Fill in the blanks:
$(a)$ 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 .........

$A$ ball is dropped from a height of $49\,m$. The wind is blowing horizontally. Due to wind,a constant horizontal acceleration is provided to the ball. Choose the correct statement$(s)$. (Take $g = 9.8\,m/s^2$)

$A$ particle moving in the $xy$ plane experiences a velocity-dependent force $\overrightarrow{F} = k(v_y \hat{i} + v_x \hat{j})$,where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\overrightarrow{v}$. If $\overrightarrow{a}$ is the acceleration of the particle,then which of the following statements is true for the particle?

$A$ particle of mass $m$ is performing $U.C.M.$ along a circle of radius $r$. The relation between centripetal acceleration $a$ and kinetic energy $E$ is given by

$A$ projectile is fired from the surface of the earth with a velocity of $5 \, m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile is fired from another planet with a velocity of $3 \, m s^{-1}$ at the same angle and follows a trajectory which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $m s^{-2}$) (Given $g = 9.8 \, m s^{-2}$):