1
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $$\theta$$ = tan$$-$$1 (x $$\times$$ 10$$-$$1). The value of x is ____________.

(Given, g = 10 m/s2)

2
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is __________ N when 6th ball just leaves the table.

3
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 = _____________.

4
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 ___________.