A block takes $t$ time to slide down a plane inclined at $45^{\circ}$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{\mathrm{t}}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$. The value of $\alpha$ is ______.

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Laws of Motion

A block takes

t

time to slide down a plane inclined at

4 5^{\circ}

to the horizontal. If the surface is made smooth (frictionless), the block takes time

\frac{t}{2}

to slide down the plane. The coefficient of friction between the block and the inclined plane is

(\frac{α}{100})

. The value of

α

is ______.

Answer: 75

Solution

On the rough incline the acceleration is

a_{1} = g (sin 4 5^{\circ} - μ cos 4 5^{\circ})

, and on the smooth incline

a_{2} = g sin 4 5^{\circ}

. Covering the same length in times

t

and

\frac{t}{2}

gives

\frac{1}{2} a_{1} t^{2} = \frac{1}{2} a_{2} (\frac{t}{2})^{2}

, so

a_{1} = \frac{a _{2}}{4}

. Then

sin 4 5^{\circ} - μ cos 4 5^{\circ} = \frac{sin 4 5 ^{\circ}}{4}

, which gives

1 - μ = \frac{1}{4}

, so

μ = \frac{3}{4} = \frac{75}{100}

and

α = 75

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Laws of Motion →

More JEE Main questions on Laws of Motion

A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field $E$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium positi …
JEE Main 2026View solution →
A large drum having radius R is spinning around its axis with angular velocity $ω$ , as shown in figure. The minimum value of $ω$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mas …
JEE Main 2026View solution →
A spring of force constant $15 N / m$ is cut into two pieces. If the ratio of their length is $1 : 3$ , then the force constant of smaller piece is ______ $N / m$
JEE Main 2026View solution →
In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $F$ required to slide the block C with constant speed is ______ N. (Used …
JEE Main 2026View solution →
A block of mass 5 kg is moving on an inclined plane which makes an angle of $3 0^{\circ}$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{3}{2}$ . The force to be applied on the block so that the block will move down witho …
JEE Main 2026View solution →
A particle of mass m falls from rest through a resistive medium having resistive force, $F = - kv$ , where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time(t)?
JEE Main 2026View solution →