How can a charged hollow sphere induce charge on a neutral conducting sphere kept inside it?

In case of a charged conducting hollow sphere charge resides on the surface and the field is radially outwards or inwards depending on the charge.Due to the symmetric consideration field inside the hollow sphere is zero.Now if I placed a neutral sphere inside the hollow sphere how does the neutral sphere accqiures induced charges with out the presence of electric fied.This is the situation given in my textbook about a spherical capacitor with outer shell charged and inner shell earthed.Its given that outer shell induces charge on inner shell.How is this possible?

You are correct in observing that electric field inside the hollow sphere is zero throughout. However the electric potential is constant. And its value is given by - $$V = \frac{kQ}{R}$$ where V is the potential, R is the radius of the charged sphere and k is the constant from Coulomb's equation.
If the inner sphere is not grounded, there would be no charge induced on the inner sphere. Note that in this case, the potential is given by the formula shown above. But as soon as you ground the inner sphere, you are ensuring that its potential is always zero(The Earth is always taken as zero potential and therefore when you ground or earth something, you are setting its potential to be zero). If there are no charges induced on the smaller sphere, the potential would not be zero but would be V as described above. With this information you can calculate the charge on the inner sphere. If the radius of the inner sphere is r and the charge on the inner sphere is q then - $$\frac{kQ}{R} - \frac{kq}{r} = 0$$ which gives $$q = -\frac{rQ}{R}$$.