Question 1 :
Two bodies are projected vertically upwards from one point with the same initial velocities {tex} v _ { 0 } \mathrm { m } / \mathrm { s } . {/tex} The second body is thrown {tex} \tau {/tex} s after the first. The two bodies meet after time
Question 2 :
A ball is thrown vertically upwards from the ground. It crosses a point at the height of 25 m twice at an interval of 4 second. The ball was thrown with the velocity of (<em>g</em> = 10 m/s<sup>2</sup>)
Question 3 :
The minimum velocity (in ms<sup>-1</sup>) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is -
Question 4 : From a canon mounted on a wagon at height H from ground, a shell is fired horizontally with a velocity {tex}v_{0}{/tex} with respect to canon. The canon and wagon has combined mass M and can move freely on the horizontal surface. The horizontal distance between shell and canon when the shell touches the ground is <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d58049841fcca588ca355f6" />
Question 5 :
A body of mass 1 kg starts moving from rest at t = 0, in a circular path of radius 8 m. Its kinetic energy varies as a function of time as KE = 2t<sup>2</sup> J, where t is in seconds. Then -
Question 6 :
On a long horizontally moving belt, a child runs to and fro with a speed 9 km h<sup>-1</sup> (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h<sup>-1</sup>.
For an observer on a stationary platform outside, what is the time taken by the child to go from father to mother and back to father is
Question 7 :
Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km $h^{-1}$ in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is
Question 8 :
Which of the following statement is true if a body moves in a semicircular track whose radius is R:
(a) 2R is the displacement of the body
(b) {tex} \pi {/tex}R is the distance traveled by the body
(c) Both (a) and (b) are correct
(d) None of the above
Question 9 :
A projectile is fired vertically upwards with an initial velocity {tex} u {/tex} After an interval of {tex} T {/tex} seconds a second projectile is fired vertically upwards, also with initial velocity {tex} u {/tex}.
Question 10 :
A body executing uniform circular motion has at any instant its velocity vector and acceleration vector
Question 11 :
A vector $\vec{A}$ has magnitude of $3$ units and it points towards east while another vector $\vec{B}$ has magnitude of $4$ units and it points towards north.The ratio between $\vec{A} \cdot\vec{B}$ and $|\vec{A}\times\vec{\mathrm{B}}|$ is:<br/>
Question 12 :
If $\overrightarrow{P}$ is directly vertically upwards and $\overrightarrow{Q}$ is directed towards north then direction of $\overrightarrow{P} \times \overrightarrow{Q}$ vector is directed towards :
Question 13 :
If $\vec {P}\times \vec {Q} = \vec {0}$ and $\vec {Q} \times \vec {R} = \vec {0}$, then the value of $\vec {P}\times \vec {R}$ is
Question 14 :
A force $-F\ \widehat{k} $ acts on O, the origin of the coordinate system.The torque about the point (-1,1) is
Question 15 :
An electron is moving with speed $2\times10^{5}m/s$ along the positive $\mathrm{x}$-direction in the presence of magnetic induction $\overline{B}=(\overline{i}+4\overline{j}-3\overline{k})T$. The magnitude of the force experienced by the electron in newtons is $(\mathrm{e}=1.6\times 10^{-19}C)$<br>
Question 16 :
If $ \overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow C = \overrightarrow C \times \overrightarrow A $ then $ \overrightarrow A + \overrightarrow B + \overrightarrow C $ is equal to:
Question 17 :
The linear velocity of a rotating body is given by $\vec{v}=\vec{\omega}\times\vec{r}$, where $\vec{\omega}$ is the angular velocity and $\vec{r}$ is the radius vector. The angular velocity of a body is $\vec{\omega}=\hat{i}-2\hat{j}+2\hat{k}$ and the radius vector $\vec{r}=4\hat{j}-3\hat{k}$, then $\begin{vmatrix}\vec{v}\end{vmatrix}$ is:
Question 18 :
Force acting on a particle is $\begin{pmatrix}2\hat {i}+3\hat {j}\end{pmatrix}N$. Work done by this force is zero, when the particle is moved on the line $3y+kx=5$. Here value of $k$ is<br>
Question 19 :
If $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}$ & $\displaystyle \vec{b}=\hat{j}-\hat{k},$ then the vector $\displaystyle \vec{c}$ such that $\displaystyle \vec{a}.\vec{c}=3$ & $\displaystyle \vec{a}\times \vec{c}=\vec{b}$ is
Question 20 :
For three non-zero vectors $\vec{a}$, $\vec{b}$, $\vec{c}$ the relation $\left |(\vec{a}\times \vec{b}).\vec{c} \right |$ =$\left | \vec{a} \right |\left | \vec{b} \right |\left | \vec{c} \right |$ will hold true if and only if:
