A charged particle of mass $m = 2\ kg$ and charge $1μC$ is projected from a horizontal ground at an angle $\theta = 45^o$ with speed $10\ ms^{-1}$ . In space, a horizontal electric field towards the direction of projection $E = 2 \times 10^7\ NC^{-1}$ exists. The range of the projectile is......$m$
$20$
$60$
$200$
$180$
A toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\vec E .$ Due to the force $q\vec E$ , its velocity increases from $0$ to $6\,\, m s^{-1}$ in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and tlie average speed of the toy car between $0$ to $3$ seconds are respectively
A body having specific charge $8\,\mu {C} / {g}$ is resting on a frictionless plane at a distance $10\, {cm}$ from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of $100 \,{V} / {m}$ is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be $....\, S.$
A stream of a positively charged particles having $\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }$ and velocity $\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s$ is deflected by an electric field $1.8 \hat{ j } kV / m$. The electric field exists in a region of $10 cm$ along $x$ direction. Due to the electric field, the deflection of the charge particles in the $y$ direction is $...........mm$
A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V _{0}$. When it passes through the origin it enters a region having uniform electric field $\overrightarrow{ E }=- E \hat{ j }$ which extends upto $x = d$. Equation of path of electron in the region $x > d$ is
A wooden block performs $SHM$ on a frictionless surface with frequency, $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\vec{E}$ is switched-on as shown, then the $SHM$ of the block will be