1
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $$\sqrt{x}$$N as shown in figure.

The value of x = _____________.

2
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

A force on an object of mass 100 g is $$\left( {10\widehat i + 5\widehat j} \right)$$ N. The position of that object at t = 2 s is $$\left( {a\widehat i + b\widehat j} \right)$$ m after starting from rest. The value of $${a \over b}$$ will be ___________.

3
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
When a body slides down from rest along a smooth inclined plane making an angle of 30$$^\circ$$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha$$T, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $${1 \over {\sqrt x }}\left( {{{{\alpha ^2} - 1} \over {{\alpha ^2}}}} \right)$$ where x = __________.
4
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
A car is moving on a plane inclined at 30$$^\circ$$ to the horizontal with an acceleration of 10 ms$$-$$2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ______________. (Take g = 10 ms$$-$$2)